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E d i t i o n
Edited D a v i d J.
by
Daniels
The Institution of Electrical Engineers
Published by: The Institution of Electrical Engineers, London, United Kingdom © 2004: The Institution of Electrical Engineers This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts., SGl 2AY, United Kingdom While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral right of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. The CD in the back of this book includes an Evaluation Version of Mathcad® 11 Single User Edition, which is reproduced by permission. This software is a fully-functional trial of Mathcad which will expire 15 days from installation. For technical support, more information about purchasing Mathcad, or upgrading from previous editions, see http://www.mathcad.com. Mathcad is a registered trademark of Mathsoft Engineering and Education, Inc., http://www.mathsoft.com. Mathsoft Engineering & Education, Inc. owns both the Mathcad software program and its documentation. Both the program and documentation are copyrighted with all rights reserved by Mathsoft. No part of the program or its documentation may be produced, transmitted, transcribed, stored in a retrieval system, or translated into any language in any form without the written permission of Mathsoft.
British Library Cataloguing in Publication Data Daniels, David Ground-penetrating radar. - 2nd ed. - (Radar, sonar, navigations & avionics) 1 .Ground penetrating radar !.Title !!.Surface penetrating radar 621.3'848 ISBN O 86341 360 9
Typeset in India by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in the UK by MPG Books Limited, Bodmin, Cornwall
Preface to the second edition
Since the first edition o f Surface penetrating radar' was published in 1996 there has been an enormous increase in research work, in publications, in hardware developments, in equipment and in radar performance. The term ground penetrating radar (GPR) has now become the accepted terminology for the science and technology, so that it was considered more in line with current practice to title the book 'Ground penetrating radar' even though it is a direct descendant of the first edition of 'Surface penetrating radar'. Ground penetrating radar has now reached a level of maturity, but there are still more performance gains to be made. One aim of this new edition is to provide a snapshot of the enormous range of applications for GPR. The problem with snapshots is that they are fleeting and often incomplete. I hope those working in the field that have not been involved with this edition will understand that it is impossible to be encyclopaedic and that there should be sufficient references and guides to sources of information to cover any omissions. The first edition received a very encouraging response and I am particularly grateful for the interest of a number of contributors. The late Professor James Wait very kindly suggested changes to the original material in the early chapters, which improved the clarity of the presentation. I am also very grateful to Dr S. Evans from the University of Cambridge and to Dr Yi Huang from the University of Liverpool, who drew my attention to inconsistencies in the text. The main aim of the second edition is to incorporate the advances in understanding and developments in techniques that have taken place since the first edition was written. The use of radar for the detection of buried objects is growing, and better understanding of the physics as well as improved technology has much enhanced the technology. GPR is now an established branch of radar technology. There is, however, much to be done in terms of improved signal processing and analysis and I hope that this flavour has permeated the second edition. The second edition describes the key elements of the subject of surface-penetrating radar, and in general terms the inter-relationship between those topics in electromagnetism, soil science, geophysics and signal processing which form a critical part of the design of a surface-penetrating radar system. The objective in writing this book is to bring together in one volume all the core information on a technique which spans
a wide range of disciplines. While much of this is available in a range of different publications, it is dispersed and therefore less accessible by virtue of the disparate nature of many of the sources. A further aim of the second edition is to provide an introduction for the newcomer to the field, as well as a useful source of further reading, information and references for the current practitioner and to bring the reader more current information. By necessity, this book provides a snapshot of the field of ground penetrating radar and it is to be expected that further developments in hardware and signal processing techniques will incrementally improve the performance and extent of applications. If this book helps the newcomer to assess the potential of the technique correctly and apply it effectively, its purpose will be well served. Several examples may illustrate the reason for the previous comment. A decade or more ago a suggestion was made that a particular ground-probing radar and its operator could detect targets the size of golf balls at a depth of 8 m. Clearly the wavelengths capable of propagating to 8 m would be so much larger than a golf ball sized target that the radar cross-sectional area of the latter would fade into insignificance, even noise. The persuasiveness of the claimant and the lack of understanding of basic physics on the part of the potential users enabled this kind of claim to be seriously proposed. Unfortunately, such claims are still being made and there are still enough gullible people who are being dazzled by the prospects. Recently, claims were made in the US that a ground penetrating radar had been developed 'that can provide threedimensional images of objects up to 45.7 m below the surface of land and sea. Such a device would allow verifiers to identify underground weapons facilities, like those of concern in Libya, Iraq and North Korea. The underwater detection capability could also be used to verify treaties dealing with submarines and nuclear weapons positioned on the seabed'. How well GPR would propagate through sea water is an interesting question given the known attenuation of sea water at radar frequencies. A careful analysis of some of the claims about the same radar was published by Tuley (2002). It is, however, concerning that such claims are still being made when it is clear that the basic physics has been well understood for decades. Therefore a secondary objective in preparing this volume has been to provide a source of information which will allow potential users to assess the merits of claims, sound or otherwise. GPR is, like all other engineering techniques, firmly based on physical principles, which must be understood if the technique is to be properly applied. In reality a metre of wet clay or salt water is still largely opaque, even to the latest radar hardware, however well provisioned with arrays of microprocessors, artificial intelligence and neural networks. It is hoped that the second edition may provide useful material for the expert or advanced practitioner in the discipline as many of the new contributions are by leaders in the field. The treatment of the subject is generally at that of first year undergraduate level, although some chapters may require a deeper knowledge of antenna and EM wave theory. The aim has been to provide a treatment which is readily accessible, Because colour is expensive to produce, the second edition has line drawings and greyscale illustrations and is a hardback edition. However, additional material and colour images as well as audio visual (AV) files are contained on the
accompanying CD. The following software is needed to access the CD: Microsoft™ Word 2000, Microsoft™ Powerpoint 2000 and Media Player™ for the MPEG and video clips and Paint Shop Pro™. There is also an evaluation copy of MathCad™ to run the MathCad simulations, although both the signal and image processing toolboxes are needed for some worksheets. After an introduction in Chapter 1 to set the scene, the general system considerations are discussed in Chapter 2. Chapter 3 considers some aspects of modelling, which is now a key means of evaluating both capability and data. Chapter 4 provides an introduction to the dielectric properties of earth materials and includes a consideration of the suitability of soils. The characteristics of antennas suitable for use in SPR systems are described in Chapter 5, and this is followed in Chapter 6 by a description of the various modulation techniques. Chapter 7 reviews the variety of signal processing options currently available. Indications are given of the range of options available and descriptions of how various workers have approached their design and implementation for a given application. The applications of the technology are reviewed in Chapter 8 (Archaeology), Chapter 9 (Civil engineering), Chapter 10 (Forensic applications), Chapter 11 (Geophysical applications), Chapter 12 (Mine detection), Chapter 13 (Utilities) and Chapter 14 (Remote sensing). Chapter 15 briefly considers the selection of equipment but, unlike the first edition, directs the reader to the websites of the companies concerned. Chapter 16 considers the licensing, radiological and EMC aspects of GPR and Chapter 17 details additional bibliographic material.
Reference TULEY, M. T., RALSTON, J. M., ROTONDO, F. S., ANDREWS, A. M., and ROSEN, E. M.: 'Evaluation of EarthRadar unexploded ordnance testing at Fort A. P. Hill, Virginia', IEEEAerosp. Electron. Syst. Mag., 2002,17, (5), pp. 10-12
Acknowledgments
I am extremely grateful for the help that I received from many fellow workers in the field of ground penetrating radar. In particular, I would like to thank those who provided individual contributions to both the first and second editions. I would also like to express my thanks and appreciation to the Directors of ERA Technology Ltd, UK, both for their support of research and development of the technology and for their assistance with the preparation of the first and second editions. I would like to thank my colleagues at ERA Technology, whose work on various programmes at various times provided the wherewithal to develop GPR techniques. In particular, I would like to thank Dr Jon Dittmer, Nigel Hunt, Paul Curtis, Dr Raj an Amin, Dr Duncan Brooks, Vince Brooker, Kevin Targett, Stefan Jennings, Giles Capps, Brian Kay, Oscar Mitchell, Ken Mann and Nick Frost and Dr Neil Williams, whose support for the technology has been invaluable. I am grateful to Pam Wheeler, who enthusiastically and patiently typed the manuscript, and to Shirley Vousden, who prepared all of the figures for the first edition. When the first edition was published, I received many favourable comments on the concept. However, various errors somehow crept through the reviewing and proofreading process, and for these I must apologise. I believe that the second edition has removed these. I am particularly grateful to the late Professor James Wait of the University of Arizona, whose review and correspondence I really appreciated. I would also like to thank Dr Stan Evans of the University Engineering Department, Cambridge, and DrYi Huang of the University of Liverpool for their help and comments on the first edition which greatly enhanced the second edition.
Contributors
First edition Dr S. Abrahamson M. Bartha H. F. Scott Prof. J. Bungey Dr R. de Vekey Dr P. Hanninen Dr R. A. van Overmeeren Dr J. K. van Deen Dr S. Tillard Dr J. Fidler Mr D. L. Wilkinson Dr J. Cariou Dr G. Schaber Prof. T. Haglars Ms F. Nicollin The following companies and people provided information on equipment for the first edition: Greg Mills of GSSI (US), Sensors and Software (Canada), Redifon (UK), ERA Technology (UK), NTT (Japan) and MALA (Sweden).
Second edition I am extremely grateful for the contributions to the second edition. Given the growth of GPR research, it is no longer possible for any individual to cover the complete field of GPR, and the input of the various contributors to the second edition provides some coverage of the extent of the growth of the subject. Contact details for the contributors to the second edition are included below.
Dr Steven A. Arcone ERDC/US A CRREL 72 Lyme Road Hanover, NH 03755, United States of America T ++1 603 646 4368 F ++1 603 646 4644 [emailprotected]
Dr Nigel J. Cassidy Principal Research Fellow Department of Applied and Environmental Geophysics Group School of Earth Sciences and Geography Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom T ++1782 583180 F ++1 782 583737 [emailprotected]
Dr Chi-Chih Chen Research Scientist ElectroScience Laboratory, Ohio State University Electrical Engineering Department 1320 Kinnear Road, Columbus, Ohio, 43212, United States of America T ++1 +614-292-7981 F ++1 +614-292-7297 Chen. [emailprotected]
Dr Richard J. Chignell Technical Director, PipeHawk pic Systems House, Mill Lane, Alton, Hampshire, GU34 2QG, United Kingdom T ++44 1420 590990 F ++44 1420 590920 richard. chignell@pipehawk. com
David J. Daniels Chief Consultant, Sensors, Electronic Systems ERA Technology Limited Cleeve Road, Leatherhead, Surrey, KT22 7SA, United Kingdom T +44 1 372 367 084 F +44 1372 367 081 [emailprotected] Les Davis President, Terad Ltd 3509 Mississauga Road, Mississauga, Ontario, LSL 2R9, Canada T ++905 820 7643 F ++905 820 7643 terad@symatico. ca Dr Xavier Derobert Researcher, Division for Soil Mechanics and Site Surveying Laboratoire Central des Ponts et Chaussees, BP 4129-44341 Bouguenais, France T 00+33+2 40 84 59 11 F 00 +33 +2 40 84 59 97 [emailprotected] Dr Jon K. Dittmer Principal Engineer, Electronic Systems ERA Technology Limited Cleeve Road, Leatherhead, Surrey, KT22 7SA, United Kingdom T +44 (0)1372 367069 F +44(0)1372 367081 [emailprotected] Dr James A. Doolittle Research Soil Scientist, United States Department of Agriculture-Natural Resources Conservation Service (USDA-NRCS) 11 Campus Boulevard Suite 200,
Newtown Square, PA 19073, United States of America T ++1 610-557-4233 F ++1 610-557-4136 [emailprotected] Dr Martin W. Fritzsche Research Scientist, Machine Perception Lab DaimlerChrysler Research & Technology, PO Box 2360, D-89013 UIm, Germany T ++49-(0)731-505-2114 F ++49-(0)731-505-4105 [emailprotected] Prof. Svein-Erik Hamran Professor, Department of Geoscience University of Oslo Postboks 1047 Blindern, N-0316 Oslo, Norway T ++47 99 02 79 43 F ++47 22 85 42 15 [emailprotected] Dr Yi Huang Associate Professor, Department of Electrical Eng & Electronics University of Liverpool, Liverpool L69 3GJ, United Kingdom T +44 151794 4521 F +44 151794 4540 [emailprotected] Dr Henrique Lorenzo Associate Professor, Department of Natural Resources & Environmental Engineering University of Vigo, EUET Forestal. Campus A Xunqueira s/n. 36005 Pontevedra, Spain T +34 986 801 935 F +34 986 801 907 [emailprotected]
Dr Christiane Maierhofer Head of Group, BAM Bundesanstalt fiir Materialforschung und - priifung Federal Institute for Materials Research and Testing Fachgruppe IV.4 Zerstorungsfreie Schadensdiagnose und Umweltmessverfahren Division IV.4 Non-Destructive Damage Assessment and Environmental Measurement Methods Unter den Eichen, 87 D-12205 Berlin T ++49+(0)30-8104 1441 F ++49+(0)30-8104 1447 [emailprotected] Dr Cedric Martel Senior Engineer, Electronic Systems ERA Technology Limited, Cleeve Road, Leatherhead, Surrey, KT22 7SA, United Kingdom T +44(0)1372 367000 F +44(0)1372 367081 [emailprotected] Dr Vega Perez Gracia Associate Professor Departamento de Resistencia de Materiales y Estructuras en Ia Ingenieria Universidad Politecnica de Cataluiia Mecanica aplicada. EUETIB. Universidad Politecnica de Cataluiia, C/Urgell 187, 08036 Barcelona, Spain T ++34 93 413 73 33 F ++34 94 413 14 21 [emailprotected] Prof. Giovanni Picardi Professor, Information and Communication Department INFOCOM Dpt University of Rome 4La Sapienza'
via Eudossiana 18-00184 Roma, Italy T +39.06.44585455 F +39.06.4873300 [emailprotected] .it Prof. Rocco Pierri Professor, Department of Information Engineering Seconda Universita' di Napoli Via Roma 29 181031, Aversa Italy T +39+0815010242 F +39+0815037370 [emailprotected] Prof. Michele Pipan Associate Professor, Department of Geological, Environmental and Marine Sciences, University of Trieste via Weiss, 1-34127 , Trieste, Italy T +39 040 5582277 F +39 040 5582290 [emailprotected] Prof. Carey Rappaport Professor, Electrical and Computer Engineering Northeastern University, Boston, MA, United States of America T ++1(617) 373-2043 (v) F ++l(617)373-8627(f) [emailprotected] Dr Juergen Sachs Associate Professor, Faculty of Electrical Engineering and Information Technology Technical University of Ilmenau, POB 100565, D-98684 Ilmenau, Germany T +49 3677 69 2623 F +49 3677 69 1113 juergen. sachs@tu-ilmenau. de Prof. Hichem Sahli Associate Professor, Department of Electronics and Information Processing
Vrije Universiteit Brussel, VUB-ETRO, Pleinlaan, 2-B-1050 Brussels, Belgium T ++32 2 629 29 16 F ++32 2 629 28 83 [emailprotected] Prof. Motoyuki Sato Professor, Center for Northeast Asian Studies Tohoku University, Kawauchi, Sendai 980-8576 Japan T +81+22 217 6075 F +81+22 217 6075 [emailprotected] Dr Timofei Savelyev Department of Electronics and Information Processing Vrije Universiteit, Brussel VUB-ETRO, Pleinlaan, 2-B-1050 Brussels, Belgium T ++32 2 629 29 16 F ++32 2 629 28 83 [emailprotected] Dr Bart Scheers Lecturer, Department of Telecommunication Royal Military Academy, Renaissancelaan 30, B-1000 Brussels, Belgium T ++32-2-7376626 F ++32-2-7376622 [emailprotected] Luc Van Kempen Department of Electronics and Information Processing Vrije Universiteit, Faculty of Applied Sciences, ETRO Department, IRIS Research Group, Pleinlaan, 2-B-1050 Brussels, Belgium T ++32 2 629 29 16 F ++32 2 629 28 83 [emailprotected]
Dr Jan van der Kruk Postdoctoral Research Associate Institute of Geophysics, Swiss Federal Institute of Technology ETH ETH-Hoenggerberg, CH-8093, Zurich, Switzerland T (41-1)6332659 F (41-1)6331065 [emailprotected] Dr Declan Vogt CSIR Division of Mining Technology, PO Box 91230, Auckland Park, 2006, South Africa T +27-11-358-0213 F +27-11-482-1214 [emailprotected]
Dr Bob Whiteley Senior Principal Geophysicist Coffey Geosciences Pty. Ltd, 142 Wicks Rd. North Ryde 2113 NSW Australia T ++612 9888 7444 F ++61 2 9888 9977 bob_whi [emailprotected] Prof. Dr Sci. Alexander G. Yarovoy Professor, International Research Centre for Telecommunications and Radar Delft University of Technology, Mekelweg 4, 2628CD Delft, The Netherlands T ++31-15-2782496 F ++31-15-2784046 [emailprotected]
I would also like to thank the IEE and their publishing staff, particularly Sarah Kramer and Wendy Hiles whose help ensured that I kept on schedule. In addition I am grateful to Leslie Bondaryk of Mathsoft, whose advice on the Mathcad worksheets was especially useful. Finally, I would like to thank my wife, Jenny, for her support, encouragement and patience during the time it has taken to write the second edition.
Contents
Preface to the Second Edition ............................................
xv
Acknowledgments ..............................................................
xix
Contributors ........................................................................
xxi
1.
Introduction ................................................................
1
1.1
Introduction ..............................................................
1
1.2
History ......................................................................
2
1.3
Applications .............................................................
3
1.4
Development ............................................................
7
1.5
Further Information Sources ....................................
9
1.5.1
Individual Websites ...................................
9
1.5.2
GPR Conferences .....................................
9
1.5.3
International Workshops on Advanced GPR ..........................................................
10
1.5.4
Institution of Electrical Engineers (UK) .....
10
1.5.5
Institute of Electrical and Electronics Engineers (USA) .......................................
10
1.5.6
SPIE Conferences ....................................
10
1.5.7
Geophysics ...............................................
11
1.5.8
Sub-surface Sensing Technologies and Applications ...............................................
11
References ..............................................................
11
1.6
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v
vi
Contents
2.
System Design ...........................................................
13
2.1
Introduction ..............................................................
13
2.2
Range ......................................................................
14
2.2.1
Introduction ...............................................
14
2.2.2
Antenna Loss ............................................
17
2.2.3
Antenna Mismatch Loss ............................
17
2.2.4
Transmission Coupling Loss .....................
17
2.2.5
Retransmission Coupling Loss .................
18
2.2.6
Spreading Loss .........................................
18
2.2.7
Target Scattering Loss ..............................
19
2.2.8
Material Attenuation Loss .........................
20
2.2.9
Total Losses ..............................................
21
2.3
Velocity of Propagation ............................................
24
2.4
Clutter ......................................................................
27
2.5
Depth Resolution .....................................................
28
2.6
Plan Resolution ........................................................
32
2.7
System Considerations ............................................
35
2.8
References ..............................................................
36
Modelling Techniques ...............................................
37
3.1
Introduction ..............................................................
37
3.2
Received Signal Levels and Probability of Detection ..................................................................
38
3.3
Basic Transmission Line Time Domain Model .........
41
3.4
Model of Antenna Radiation and Buried Target Interaction ................................................................
44
3.4.1
Model Description .....................................
44
3.4.2
Discretisation of the Structures .................
44
3.4.3
Time Domain Field Plots ...........................
45
3.
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Contents
vii
Application of Numerical Modelling for the Interpretation of Near-surface Ground Penetrating Radar .......................................................................
47
3.5.1
Practical Modelling Schemes ....................
48
3.5.2
Modelling Applications ..............................
49
3.5.3
Material Property Descriptions ..................
50
3.5.4
Antenna Design ........................................
50
3.5.5
Outer Absorbing Boundary Conditions (ABC) ........................................................
50
3.5.6
Example Applications ................................
51
3.5.7
Modelling the Response from Defects in Roadway Construction ..............................
56
Summary ...................................................
57
Modelling GPR Surface Roughness Clutter Effects for Mine Detection ....................................................
58
3.6.1
Introduction ...............................................
58
3.6.2
Target Shape Scattering Characteristics ..
60
3.6.3
Rough Surface Modelling Results .............
62
3.6.4
Summary ...................................................
66
3.6.5
Acknowledgments .....................................
67
3.7
Summary .................................................................
67
3.8
References ..............................................................
67
Properties of Materials ..............................................
73
4.1
Introduction ..............................................................
73
4.2
Propagation of Electromagnetic Waves in Dielectric Materials ..................................................
75
4.3
Properties of Lossy Dielectric Materials ...................
84
4.4
Water, Ice and Permafrost .......................................
91
4.5
Dielectric Properties of Soils and Rocks ..................
94
4.6
Suitability of Soils for GPR Investigations ................
97
4.6.1
97
3.5
3.5.8 3.6
4.
Introduction ...............................................
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viii
Contents 4.6.2 4.6.3 4.6.4
5.
GPR: a Quality Control Tool for Soil Mapping and Investigation ........................
98
Suitability of Soil Properties for GPR Investigations ............................................
98
Soil Suitability Maps for GPR Investigations ............................................
99
4.6.5
Determining the Depth to Soil Horizons .... 101
4.6.6
Determining the Depth to Bedrock ............ 102
4.6.7
Determining the Depth to Soil Water Tables ....................................................... 104
4.6.8
Measuring Soil Moisture Contents and the Movement of Water through Sandy Soils .......................................................... 105
4.6.9
Determining the Thickness of Peat Deposits .................................................... 105
4.6.10
Improving Soil-landscape Models ............. 107
4.7
Dielectric Properties of Man-made Materials ........... 108
4.8
Laboratory Measurements of Dielectric Materials ... 110 4.8.1
Introduction ............................................... 110
4.8.2
Measurement Techniques ........................ 111
4.9
Field Measurements of Soil Properties .................... 117
4.10
Summary ................................................................. 119
4.11
References .............................................................. 120
4.12
Bibliography ............................................................. 128
Antennas .................................................................... 131 5.1
Introduction .............................................................. 131
5.2
Element Antennas ................................................... 140
5.3
Travelling Wave Antennas ....................................... 147
5.4
Impulse Radiating Antennas .................................... 152
5.5
Frequency Independent Antennas ........................... 155
5.6
Horn Antennas ......................................................... 159
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Contents
6.
ix
5.7
Array Antennas ........................................................ 164
5.8
Polarisation .............................................................. 169
5.9
Dielectric Antennas .................................................. 172 5.9.1
Introduction ............................................... 173
5.9.2
Summary ................................................... 176
5.10
Summary ................................................................. 177
5.11
References .............................................................. 178
5.12
Bibliography ............................................................. 182
Modulation Techniques ............................................. 185 6.1
Introduction .............................................................. 185
6.2
Resolution of Ultra-wideband Signals ...................... 187 6.2.1
Introduction ............................................... 187
6.2.2
Consideration of Waveform Characteristics .......................................... 190
6.2.3
Definition of the Waveforms ...................... 191
6.2.4
Time Domain Wavelet Signals .................. 192
6.2.5
Noise Signals ............................................ 194
6.2.6
Comparison of Signals .............................. 194
6.2.7
Comparison of Spectra ............................. 194
6.2.8
Comparison of Signal Envelopes .............. 194
6.2.9
Comparison of Envelope Sidelobe Performance ............................................. 197
6.2.10
Summary ................................................... 197
6.3
Amplitude Modulation .............................................. 199
6.4
Frequency Modulated Continuous Wave (FMCW) .. 211
6.5
Synthesised or Stepped Frequency Radar .............. 220
6.6
Noise Modulated Radar ........................................... 224
6.7
6.6.1
Introduction ............................................... 224
6.6.2
M-sequence Radar ................................... 225
Single Frequency Methods ...................................... 237
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x
7.
Contents 6.8
Polarisation Modulation ........................................... 239
6.9
Summary ................................................................. 242
6.10
References .............................................................. 243
6.11
Bibliography ............................................................. 246
Signal Processing ...................................................... 247 7.1
Introduction .............................................................. 247
7.2
A-scan Processing ................................................... 251 7.2.1
Zero Offset Removal ................................. 252
7.2.2
Noise Reduction ........................................ 253
7.2.3
Clutter Reduction ...................................... 254
7.2.4
Time Varying Gain .................................... 255
7.2.5
Frequency Filtering ................................... 255
7.2.6
Wavelet Optimisation or Deconvolution Techniques ............................................... 256
7.2.7
Target Resonances ................................... 264
7.2.8
Spectral-analysis Methods ........................ 266
7.2.9
Examples of Processing Techniques ........ 272
7.3
B-scan Processing ................................................... 276
7.4
C-scan Processing ................................................... 277
7.5
Migration .................................................................. 278 7.5.1
Migration Technique Based on Deconvolution ........................................... 283
7.5.2
Synthetic Aperture Processing .................. 293
7.6
Image Processing .................................................... 295
7.7
Deconvolution Techniques ...................................... 298 7.7.1
Linear and Circular Deconvolution ............ 298
7.7.2
Deconvolution in UWB GPR Processing as an Ill-posed Inverse Problem ............... 300
7.7.3
Regularisation Methods and Deconvolution Algorithms ......................... 301
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Contents 7.8
7.9
7.10
8.
xi
Multi-fold, Multi-component and Multi-azimuth GPR for Sub-surface Imaging and Material Characterisation ....................................................... 310 7.8.1
Introduction ............................................... 310
7.8.2
Data Acquisition ........................................ 311
7.8.3
Data Processing ........................................ 311
7.8.4
Results ...................................................... 313
7.8.5
Discussion ................................................. 320
Microwave Tomography .......................................... 323 7.9.1
Introduction ............................................... 323
7.9.2
Formulation of the Tomographic Approach ................................................... 323
7.9.3
Key Point of Imaging: Spatial Filtering ...... 326
7.9.4
Key Point of Imaging: Resolution Limits ... 330
Minimising Clutter .................................................... 333 7.10.1
Reduction of Unwanted Diffractions and Reflections from Above-surface Objects ... 333
7.10.2
Clutter in Radar Data Caused by Reflections from External Anomalies ........ 335
7.11
Summary ................................................................. 342
7.12
References .............................................................. 343
7.13
Bibliography ............................................................. 349
Archaeology ............................................................... 353 8.1
Introduction .............................................................. 353
8.2
Fountains Abbey, UK ............................................... 354
8.3
Saqqara, Egypt ........................................................ 357
8.4
The Crypt of the Cathedral of Valencia .................... 362
8.5
Historic Masonry Structures ..................................... 366 8.5.1
Church of S. Maria Rossa, Milan, Italy ...... 367
8.5.2
Altes Museum, Berlin, Germany ............... 370
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xii
Contents 8.5.3
9.
Location of Metallic Anchors and Clamps Fixing the Facade of a Gothic Cathedral .. 374
8.6
Summary ................................................................. 376
8.7
References .............................................................. 376
8.8
Bibliography ............................................................. 379
Civil Engineering ....................................................... 381 9.1
Introduction .............................................................. 381
9.2
Roads and Pavements ............................................ 381 9.2.1
Roads in the UK ........................................ 383
9.2.2
Step-frequency Radar Technique Applied on Very-thin Layer Pavements .................. 386
9.2.3
High Resolution GPR Testing of Conduits and Pavements ......................................... 394
9.3
Concrete .................................................................. 402
9.4
Concrete Structures ................................................. 404
9.5
9.4.1
Location of Reinforcement and Tendon Ducts ......................................................... 406
9.4.2
Location of Dowels and Anchors in Concrete Highways ................................... 408
Buildings .................................................................. 410 9.5.1
Introduction ............................................... 410
9.5.2
Masonry .................................................... 411
9.5.3
Concrete System Walls and Floors ........... 411
9.5.4
Joints in Concrete System Buildings ......... 411
9.6
Tunnels .................................................................... 412
9.7
Summary ................................................................. 417
9.8
References .............................................................. 417
9.9
Bibliography ............................................................. 422
10. Forensic Applications ............................................... 423 10.1
Introduction .............................................................. 423
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Contents 10.2
10.3
xiii
Principles of GPR Forensic Search ......................... 425 10.2.1
Method ...................................................... 425
10.2.2
Graves ...................................................... 426
10.2.3
Remains .................................................... 426
10.2.4
Excavation ................................................ 427
10.2.5
Test Grave Sites ....................................... 427
Case Histories ......................................................... 429 10.3.1
Frederick West .......................................... 429
10.3.2
Marc Dutroux ............................................ 431
10.3.3
Victims of the 1918 Spanish Flu Epidemic ................................................... 433
10.3.4
Investigation of Potential Mass Grave Locations for the Tulsa Race Riot ............. 434
10.4
Summary ................................................................. 436
10.5
References .............................................................. 436
11. Geophysical Applications ......................................... 437 11.1
Introduction .............................................................. 437
11.2 11.3
Applications Relating to Frozen Materials ............... 438 Snow and Ice Research with Ground Penetrating Radar ....................................................................... 439
11.4
11.3.1 11.3.2
Introduction ............................................... 439 Transient Short-pulse and FMCW Radar ........................................................ 441
11.3.3
Firn Layering and Isochrones ................... 444
11.3.4
Crevasse Detection ................................... 449
11.3.5
Hydraulic Pathways .................................. 449
11.3.6
Bed Topography ....................................... 450
11.3.7
Lake Ice .................................................... 452
11.3.8
Future Directions ....................................... 453
GPR Sounding of Polythermal Glaciers ................... 455 11.4.1
Introduction ............................................... 455
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Contents 11.4.2
Polythermal Glacier ................................... 455
11.4.3
Radar System ........................................... 457
11.4.4
Bottom Topography .................................. 458
11.4.5
Internal Structure ...................................... 458
11.4.6
Snow Cover .............................................. 459
11.4.7
Summary ................................................... 459
11.5
The Prestige Oil Spill ............................................... 460
11.6
Peatland Investigations ............................................ 464
11.7
Soil Contamination ................................................... 465
11.8
Geological Structures .............................................. 466
11.9
Soil Erosion .............................................................. 467
11.10 Coal and Salt ........................................................... 469 11.11 Rocks ....................................................................... 471 11.12 Borehole Radar ........................................................ 475 11.12.1 Borehole Radar for Long-distance GPR Imaging In-mine ........................................ 475 11.12.2 Borehole Radar Design ............................. 476 11.12.3 Example Borehole Radar Data ................. 478 11.13 Polarimetric Borehole Radar for Characterisation of Sub-surface Fractures ......................................... 483 11.13.1 Sub-surface Fracture Characterisation ..... 483 11.13.2 Radar Polarimetry ..................................... 485 11.13.3 Field Experiment ....................................... 486 11.14 VHP Band Slimline Borehole Radar Experiences in the South African Mining Industry ........................ 489 11.14.1 Introduction ............................................... 489 11.14.2 BHR Specifications ................................... 490 11.14.3 Digital Data Acquisition ............................. 490 11.14.4 Typical Problem ........................................ 491 11.14.5 Signal and Image Processing ................... 492 11.14.6 Electromagnetic Modelling ........................ 493 This page has been reformatted by Knovel to provide easier navigation.
Contents
xv
11.14.7 Summary ................................................... 493 11.15 Summary ................................................................. 493 11.16 References .............................................................. 494 11.17 Bibliography ............................................................. 499
12. Mine Detection ........................................................... 501 12.1
Introduction .............................................................. 501
12.2
Humanitarian and Military National Programmes .... 506 12.2.1
Australia .................................................... 507
12.2.2
Belgium ..................................................... 508
12.2.3
Canada ..................................................... 509
12.2.4
European Commission Programmes ........ 510
12.2.5
France ....................................................... 511
12.2.6
Germany ................................................... 512
12.2.7
Netherlands ............................................... 512
12.2.8
Russia ....................................................... 513
12.2.9
Sweden ..................................................... 513
12.2.10 United Kingdom ........................................ 514 12.2.11 US Army Military Programme ................... 514 12.3
Performance and Test Assessment ......................... 515
12.4
Mine Detection with GPR ......................................... 520
12.5
Hand-held Mine Detection ....................................... 525
12.6
Vehicle Mounted ...................................................... 526
12.7
Airborne ................................................................... 534
12.8
12.7.1
Introduction ............................................... 534
12.7.2
The Mineseeker Airship Project ................ 534
Case Studies ........................................................... 540 12.8.1
Introduction ............................................... 540
12.8.2
Detection of Buried Landmines with GPR .......................................................... 540
12.8.3
MINETECT ................................................ 557
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Contents
12.9
12.8.4
TU Delft Research Activities in the Area of Advanced GPR Technology .................. 569
12.8.5
Lotus Project ............................................. 578
12.8.6
Data Processing for Clutter Characterisation and Removal .................. 581
Summary ................................................................. 609
12.10 References .............................................................. 610 12.11 Bibliography ............................................................. 621
13. Utilities ........................................................................ 625 13.1
Introduction .............................................................. 625
13.2
Technology .............................................................. 627 13.2.1
Pipes and Cables ...................................... 627
13.2.2
PipeHawk .................................................. 631
13.3
Array Based Utility Mapping .................................... 634
13.4
Case Histories ......................................................... 636 13.4.1
Drainage of a Football Pitch ...................... 636
13.4.2
Services on a Proposed Building Site ....... 637
13.4.3
GPR Surveying in Central London ............ 640
13.5
Surveying a Car Park ............................................... 640
13.6
Internal Inspection of Pipes ..................................... 644
13.7
Summary ................................................................. 646
13.8
References .............................................................. 646
14. Remote Sensing ......................................................... 649 14.1
Introduction .............................................................. 649
14.2
Airborne SAR Systems for Earth Sensing ............... 650
14.3
Satellite Based Systems for Earth Sensing ............. 651
14.4
Planetary Exploration ............................................... 657 14.4.1
Mars 96 Mission ........................................ 657
14.4.2
Mars 96 Project ......................................... 659
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xvii
Radar for Measuring Interplanetary Bodies ............. 663 14.5.1
Introduction ............................................... 663
14.5.2
Scientific Objectives .................................. 665
14.5.3
Reference Models ..................................... 665
14.5.4
Surface and Sub-surface Scattering Models ...................................................... 669
14.5.5
Sub-surface Interface Detection Performance ............................................. 683
14.5.6
Summary ................................................... 686
14.6
Summary ................................................................. 686
14.7
References .............................................................. 687
14.8
Bibliography ............................................................. 690
15. Equipment .................................................................. 693 15.1
15.2
Introduction .............................................................. 693 15.1.1
Survey Methods ........................................ 696
15.1.2
Site Characteristics ................................... 698
15.1.3
Surface Characteristics ............................. 699
15.1.4
Material Characteristics ............................ 699
15.1.5
Target Characteristics ............................... 699
List of Companies Offering GPR Technology .......... 701
16. Regulation, Radiological Aspects and EMC ............ 703 16.1
Regulation ................................................................ 703 16.1.1
Europe ...................................................... 703
16.1.2
United States ............................................ 705
16.1.3
Summary ................................................... 707
16.2
Radiological Aspects ............................................... 707
16.3
EMC ......................................................................... 708
16.4
Summary ................................................................. 712
16.5
References .............................................................. 713
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Contents
17. Bibliography ............................................................... 715 Glossary of Terms ............................................................ 717 List of Symbols ................................................................. 721 Index .................................................................................. 723
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Chapter 1
Introduction
1.1
Introduction
The possibility of detecting buried objects remotely has fascinated mankind over centuries. A single technique which could render the ground and its contents clearly visible is potentially so attractive that considerable scientific and engineering effort has gone into devising suitable methods of exploration. As yet, no single method has been found to provide a complete answer, but seismic, electrical resistivity, induced polarisation, gravity surveying, magnetic surveying, nucleonic, radiometric, thermographic and electromagnetic methods have all proved useful. Ground penetrating, -probing or surface-penetrating radar has been found to be a specially attractive option. The subj ect has a special appeal for practising engineers and scientists in that it embraces a range of specialisations such as electromagnetic wave propagation in lossy media, ultra wideband antenna technology and radar systems design, discriminant waveform signal processing and image processing. Most ground penetrating radars are a particular realisation of ultra-wideband impulse radar technology. Skolnik [1] considers that 'the technology of impulse radar creates an exciting challenge to the innovative engineer' and ground probing radar to have been a successful commercial venture although on a smaller scale than conventional radar applications. The terms' ground penetrating radar (GPR)',' ground-probing radar',' sub-surface radar' or 'surface-penetrating radar (SPR)' refer to a range of electromagnetic techniques designed primarily for the location of objects or interfaces buried beneath the earth's surface or located within a visually opaque structure. The term 'surfacepenetrating' is preferred by the author as it describes most accurately the application of the method to the majority of situations including buildings, bridges, etc. as well as probing through the ground. However, the description 'ground penetrating radar' will be used to describe the technique as it has become almost universally accepted. The technology of GPR is largely applications-oriented and the overall design philosophy, as well as the hardware, is usually dependent on the target type and the material
of the target and its surroundings. The range of applications for GPR methods is wide and the sophistication of signal recovery techniques, hardware designs and operating practices is increasing as the technology matures. More recent developments include airborne and satellite surveying as well as high-speed survey from vehicle mounted radars. There has been an enormous growth in research into GPR and it has not been possible to cover all the groups working in the field in this edition. Those working in the area will be able to use the publications of the IEE, IEEE, SPIE, the GPR conferences and workshops, Geophysics and other sources to ensure that they are fully up to date with the field. These are listed at the end of this chapter. This second edition represents a snapshot of technology, practice and future developments in the field at the time of publication but it is not exhaustive. The first edition of the book was intended as an introduction to the subject. Most of the basic material has been retained and is aimed at the growing number of potential users who wish to gain an introductory understanding of the method at a level appropriate to the first year of undergraduate studies. It is assumed that, whatever the reader's background, be it in geophysics, civil engineering or archaeology, he or she has a basic understanding of physics and geophysics and understands that radar is an active measurement technique which allows the ranging and detection of targets. Although each chapter has been written in the form of a self-contained section relevant to its particular topic, the overall aim of the author has been to create a sufficiently wide-ranging treatment that will enable interested readers to investigate areas of particular interest in greater depth. To assist the reader, a list of suitable references is provided at the end of each chapter. The second edition develops some of the areas in more depth and hopefully will be found useful for those developing particular specialities. Following early laboratory developments in the late 1960s and 1970s in both the US and UK commercial equipment has become more freely available and the GSSI Impulse Radar has become the most widely used commercial system. More recently, alternative equipment using various modulation techniques has become available and the market is expanding. However, the impulse radar has been the most successful design to date and probably accounts for 95% of the units in operation in the field. The general structure of this volume is based on an earlier paper which was published in a special edition of the IEE Proceedings Part F [2] by Daniels et al. (1988), which served as an introduction to GPR techniques. This still serves well as a primer and the introduction is still relevant and is quoted below. GPR in the hands of an expert provides a safe and noninvasive method of conducting speculative searches without the need for unnecessary disruption and excavation. GPR has significantly improved the efficiency of the exploratory work that is fundamental to the construction and civil engineering industries, the police and forensic sectors, security/intelligence forces and archaeological surveys.
1.2
History
The first use of electromagnetic signals to determine the presence of remote terrestrial metal objects is generally attributed to Hiilsmeyer in 1904, but the first description
of their use for location of buried objects appeared six years later in a German patent by Leimbach and Lowy. Their technique consisted of burying dipole antennas in an array of vertical boreholes and comparing the magnitude of signals received when successive pairs were used to transmit and receive. In this way, a crude image could be formed of any region within the array which, through its higher conductivity than the surrounding medium, preferentially absorbed the radiation. These authors described an alternative technique, which used separate, surface-mounted antennas to detect the reflection from a sub-surface interface due to ground water or to an ore deposit. An extension of the technique led to an indication of the depth of a buried interface, through an examination of the interference between the reflected wave and that which leaked directly between the antennas over the ground surface. The main features of this work, namely CW operation, use of shielding or diffraction effects due to underground features, and the reliance on conductivity variations to produce scattering, were present in a number of other patent disclosures, including some intended for totally submerged applications in mines. The work of Hiilsenbeck [3] in 1926 appears to be the first use of pulsed techniques to determine the structure of buried features. He noted that any dielectric variation, not necessarily involving conductivity, would also produce reflections and that the technique, through the easier realisation of directional sources, had advantages over seismic methods. Pulsed techniques were developed from the 1930s onwards as a means of probing to considerable depths in ice [4, 5], fresh water, salt deposits [6], desert sand and rock formations [7, 8]. Probing of rock and coal was also investigated by Cook [9,10], and Roe and Ellerbruch [11], although the higher attenuation in the latter material meant that depths greater than a few metres were impractical. A more extended account of the history of GPR and its growth up to the mid 1970s is given by Nilsson [12]. Renewed interest in the subject was generated in the early 1970s when lunar investigations and landings were in progress. For these applications, one of the advantages of ground penetrating radar over seismic techniques was exploited, namely the ability to use remote, noncontacting transducers of the radiated energy, rather than the ground contacting types needed for seismic investigations. Remote transducers are possible because the dielectric impedance ratio between free space and soil materials, typically from 2 to 4, is very much less than the corresponding ratio for acoustic impedances, by a factor which is typically of the order of 100. From the 1970s until the present day, the range of applications has been expanding steadily, and now includes building and structural nondestructive testing, archaeology, road and tunnel quality assessment, location of voids and containers, tunnels and mineshafts, pipe and cable detection, as well as remote sensing by satellite. Purposebuilt equipment for each of these applications is being developed and the user now has a better choice of equipment and techniques.
1.3
Applications
Recent progress has been one of continuing technical advance largely applicationsdriven, but as the requirements have become more demanding, so the equipment, techniques and data processing methods have been developed and refined.
GPR has been used in the following applications: archaeological investigations borehole inspection bridge deck analysis building condition assessment contaminated land investigation detection of buried mines (anti-personnel and anti-tank) evaluation of reinforced concrete forensic investigations geophysical investigations medical imaging pipes and cable detection planetary exploration rail track and bed inspection remote sensing from aircraft and satellites road condition survey security applications snow, ice and glacier timber condition tunnel linings wall condition GPR has been very successfully used in forensic investigations. The most notorious cases occurred in the United Kingdom in 1994, when the grave sites, under concrete and in the house of Fred West, of the victims of the serial murderer were pinpointed. In Belgium, the grave sites of the victims of the paedophile, Dutroux, were detected in 1996. Both these investigations were carried out using GPR developed by ERA Technology and the ERA team. Archaeological applications of GPR have been varied, ranging from attempts to detect the Ark to the exploration of Egyptian and North American Indian sites as well as castles and monasteries in Europe. The quality of the radar image can be exceptionally good, although correct understanding normally requires joint interpretation by the archaeologists and radar specialists. Abandoned anti-personnel land mines and unexploded ordnance are a major hindrance to the recovery of many countries from war. Their effect on the civilian population is disastrous, and major efforts are being made by the international community to clear the problem. Most detection is done with metal detectors, which respond to the large amount of metallic debris in abandoned battlefield areas and hence have difficulty in detecting the minimum metal or plastic mine. GPR technology is being applied to this problem as a means of reducing the false alarm rate and providing improved detection of low metal content mines. GPR has been used for surveying many different types of geological strata ranging from exploration of the Arctic and Antarctic icecaps and the permafrost regions of North America, to mapping of granite, limestone, marble and other hard rocks as well as geophysical strata.
The thickness of the various layers of a road can be measured using radar techniques. The great advantage is that this method is nondestructive and high speed (>40 km/h) and can be applied dynamically to achieve a continuous profile or rolling map. The accuracy of calibration tends to decrease as a function of depth because of the attenuation characteristics of the ground. The accuracy may be quite high (i.e. a few millimetres) for the surface wearing course but will degrade to centimetres at depths of one metre. While most GPR systems are used in close proximity to the ground, airborne systems have been able to map ice formations, glaciers, and penetrate through forest canopy. Airborne GPR, processed using synthetic aperture techniques, has been used to detect buried metallic mines from a height of several hundred metres in SAR (synthetic aperture radar) mode. In addition the SIR-C satellite SAR radar has imaged buried artefacts in desert conditions, and the JPL website http://southport.jpl.nasa.gov/sir-c/ is an important source of radar imagery. The main operational advantages of the technique can be described as follows. The antennas of a GPR do not need to be in contact with the surface of the earth, thereby allowing rapid surveying. Antennas may be designed to have adequate properties of bandwidth and beam shape, although optimum performance, especially where a small antenna-to-ground surface spacing is involved, will usually be obtained only by taking into account details of the geometry and the nature of the ground. Signal sources are available which can produce sub-nanosecond impulses or alternatively which can be programmed to produce a wide range of modulation types. In general, any dielectric discontinuity is detected. Targets can be classified according to their geometry: planar interfaces; long, thin objects; localised spherical or cuboidal objects. The radar system can be designed to detect a given target type preferentially and is potentially capable of producing an image of the target in three dimensions, although little work has been done on this aspect of image presentation. The signal attenuation at the desired operating frequency is the main factor to be considered when assessing the usefulness of radar probing in a given material. As a rule, material that has a high value of low-frequency conductivity will have a large signal attenuation. Thus gravel, sand, dry rock and fresh water are relatively easy to probe using radar methods, while salt water, clay soils and conductive ores or minerals are less so, but a reduction in the transmitted frequency means that even these materials can be adequately investigated, though at the expense of a reduced resolution between targets. GPR will work successfully in fresh water so that water content is not a complete guide to achievable penetration range. GPR relies for its operational effectiveness on successfully meeting the following requirements:
(a) (b)
efficient coupling of electromagnetic radiation into the ground; adequate penetration of the radiation through the ground having regard to target depth;
(c) (d)
obtaining from buried objects or other dielectric discontinuities a sufficiently large scattered signal for detection at or above the ground surface; an adequate bandwidth in the detected signal having regard to the desired resolution and noise levels.
The essence of the technique is no different from that of conventional, free-space radar, but of the factors that affect the design and operation of any radar system the four requirements indicated earlier take on an additional significance in ground penetrating radar work. Specifically, propagation loss, clutter characteristics and target characteristics are distinctly different. The radar technique is usually employed to detect backscattered radiation from a target. Forward scattering can also yield target information, although for sub-surface work at least one antenna would need to be buried, and an imaging transform would need to be applied to the measured data. The designer of radar for ground-penetrating applications has two problems, not necessarily encountered by the designer of a conventional radar: designing to a limited budget and overcoming difficult signal recovery problems primarily associated with signal to clutter ratio. As the cost of processing falls, the designer can consider signal processing strategies previously thought uneconomic, and this will be likely to have a significant effect on system design and hence commercial viability. For example, in early radars for ground-penetrating applications, it was considered necessary to employ wideband antennas with linear phase response, because of the resultant difficulties in deconvolving the antenna response. However, it is now possible to correct for nonlinear phase characteristics, if desired, at a reasonable cost by using appropriate signal processing techniques implemented in software. GPR is vulnerable to extremely high levels of clutter at short ranges, and this rather than signal/noise recovery is its major technical handicap. The system to be specified should take this into account. Some basic guidelines can be suggested for the user of radar for ground probing applications. It is important to define clearly the target parameters. There is a considerable difference between the target response from a buried pipe, a buried mine, a void or a planar interface. This has a major impact on antenna design, polarisation state and signal processing strategy and should be exploited. The resolution and depth requirement needed should be clearly identified. This in turn sets the frequency and bandwidth of operation, which then influence the choice of modulation technique and hence the hardware design. The costs of overspecification can be considerable and the physics of propagation should be kept in mind. The transmission loss characteristics will affect the selection of a system. It is unlikely that synthetic aperture or holographic schemes will work well in high-loss materials. The display requirements can have a major impact on equipment costs. This has a fundamental bearing on the type of signal processing required. Image presentation obviously needs different signal processing from that required for target identification and classification. Signal processing must take account of the needs of the user and as
much as possible of the interpretation process should be done automatically, if GPR techniques are to gain widespread acceptance for routine use in, say, pipe and cable location. Recent developments have shown that it is possible to use a simple audio output for the man-machine interface, and this is discussed in Chapter 12. The operational requirements are such that physical decoupling of the antenna from the surface should only be carried out where strictly necessary. This is not simply for reasons of power transfer but also for reduction of clutter and efficiency of transfer. Some of the ancillary requirements of an operational ground penetrating radar system need more consideration. There is a need for an accurate, small-scale, lowcost position referencing system for use with radar for ground-penetrating survey techniques. For utilities it will be most important that data can be related to a true geographic reference, particularly when filed on digital mapping systems and used to define areas of safe working. It will be necessary to provide some means of scanning the antenna. Obviously a basic approach is the hand-held device but this places severe limitations on the signal processing strategies. Alternatives are robotic arms and miniature tracked vehicles; the former may limit the area of search but may be cheaper for surveying road and pavement areas, while the latter may be the most flexible, but will require accurate position referencing. If the radar is to provide its operator with an image of targets under the ground surface, then online processing will be needed. With the projected developments in advanced microprocessors it is likely that significant amounts of online processing will soon become economically feasible.
1.4
Development
The key future development area will be signal processing and image recognition methods, and this requires development of core strategies generally based on deconvolution techniques. The future of GPR is considered to be based on short range geophysical exploration and nondestructive investigation. For short range geophysical exploration ground penetrating radar has already achieved some significant results. It is, however, in the area of nondestructive investigation of structures such as tunnels, roads, buildings and other examples of physical infrastructure of modern civilisation that GPR has an increasingly important role to play. Potential customers could be energy and communications utilities, mineral resource exploration organisations, civil engineering organisations, nondestructive testing companies, military and security organisations, architects, archaeologists and scientific research establishments. Many of these organisations only wish to purchase surface-penetrating radars provided the price is within reasonable limits, and they may prefer to hire the services of a specialist surveying organisation or alternatively hire equipment. It is likely that the commercial definition of a reasonable price for either commercial equipment, hire or service, will be different from the military definition of a reasonable price for a radar.
In addition, the experience of many of those commercial organisations in relation to electronic equipment is of mainstream suppliers of conventional equipment. Suppliers of production quantities achieve economies of scale which are unlikely to apply in the case of a radar for ground-penetrating applications. The designer of surface-penetrating radars must therefore take into account the type of markets which exist at present. However, the success of the current commercial radars is encouraging and suggests that evolutionary design processes could widen the market. One possible design strategy for GPR could be seen as the development of a modular system. With this approach, frequency range, and hence antenna type, can be modified simply, and signal processing can be selected by choice of target and display format. This would allow economy in development and of production and result in a more commercially attractive product. The potential cannot be overlooked of increasingly powerful microprocessors available at low cost, capable of carrying out sophisticated signal processing and then displaying the results so that interpretation by an expert is less important. This potential should provide the technology necessary for radar for ground-penetrating applications to gain wide acceptance as a valuable investigative tool capable of being used by the nonspecialist. However, the pattern recognition capability of the human brain is still unequalled and may remain so for many decades. GPR is one of a very few methods available which allows the inspection of objects or geological features which lie beneath an optically opaque surface. Much funding to date has come from industries in the civil sector with a direct interest in the information that can be derived from ground penetrating radar exploration: the utilities (gas, electricity, water, telecommunications), oil and gas exploration companies, geophysical survey groups. The total expenditure is still small when compared with the investment, largely from military sources, in free space radar developments. However, it is generally considered that GPR has been a successful commercial venture even if its market sector value is not as large as some of the radar applications. With improvements in the performance of ground penetrating radar systems will come wider commercial acceptance. The challenge for the designer is to speed up the rate of development. Ground penetrating radar technology will become more firmly established as its benefits are perceived and realised by users distinctly different from those of conventional free-space radar technology. Spectrum usage is becoming ever more contested and hence licensing is becoming a key issue. The FCC and ETSI are in the process of regulating the use of the radio frequency spectrum in a way which will challenge the manufacturers and users of GPR. The reality is that GPR has caused no interference problems and much of the pressure by other users is based on unwarranted nervousness. However, new developments in noise radar and pseudo-random coded waveforms promise to further reduce the potential for interference to other spectrum users. This is discussed in Chapter 6. Although GPR has achieved some spectacular successes, it would be unrealistic to leave the impression that GPR is the complete solution to the users' perceived
problem (whatever that may be). A GPR will detect, within the limits of the physics of propagation, all changes in electrical impedance in the material under investigation. Some of these changes will be associated with wanted targets, while others may not be. The radar has, in general, no way of discriminating, and much of the skill of the successful user currently comes from forming a conclusion from both the radar image and site intelligence. The more successful operators routinely exercise this discipline and procedure. The potential user should therefore understand both the capabilities and limitations of the method. This book will have achieved that objective if the user employs radar in the right place at the right time in parallel with other geophysical exploration methods.
1.5 Further information sources Further useful information can be gained from a variety of sources, and a list is given below of useful websites and institutions. A list of publications and sources is included in each Chapter. 1.5.1
Individual
websites
Some of these websites are solely GPR, while others contain useful material related to GPR: Dr David Noon's website at http://www.cssip.uq.edu.au/staff/noon/gprlist.html Prof Gary Olhoeft's website on http://www.g-p-r.com/ ARIS website at http://demining.jrc.it/aris/ DeTeC website at http://diwww.epfl.ch/lami/detec/detec.html Eudem website at http://www.eudem.vub.ac.be/ 1.5.2
GPR conferences
GPR 2000 - Gold Coast, Australia, 8th International Conference on Ground Penetrating Radar. David Noon, University of Queensland, email: [emailprotected] GPR '98 - Lawrence, Kansas, USA, 7th International Conference on Ground Penetrating Radar. Dr. Richard Plumb, University of Kansas, email: [emailprotected] GPR '96 - Sendai, Japan, 6th International Conference on Ground Penetrating Radar. Prof. Motoyuki Sato, Tohoku University, email: [emailprotected] GPR '94 - Kitchener, Ontario, Canada, 5th International Conference on Ground Penetrating Radar. David Redman, Sensors & Software, email: [emailprotected] GPR '92 - Rovaniemi, Finland, 4th International Conference on Ground Penetrating Radar. Pauli Hanninen, Geological Survey of Finland GPR '90 - Lakewood, Colorado, USA, 3rd International Conference on Ground Penetrating Radar. Prof. Gary Olhoeft, Colorado School of Mines, email: golhoeft@mines. edu
1988 - Gainesville, Florida, USA, 2nd International Symposium on Geotechnical Applications of Ground Penetrating Radar. Mary Collins, University of Florida, email: [emailprotected] 1986 - Tifton, Georgia, USA, 1st International Conference on Geotechnical Applications of Ground Penetrating Radar 7.5.3
International workshops on advanced GPR
IWAGPR Delft 01 - 1st International Workshop on Advanced Ground Penetrating Radar (International Workshop) published in 'Subsurface sensing technologies and applications' (Kluwer, June 2001) IWAGPR Delft 03 - 2nd International Workshop on Advanced Ground Penetrating Radar (International Workshop). Web link: http://irctr.et.tudelft.nl/IWAGPR/ 1.5.4
Institution of Electrical Engineers (UK)
See also Radar 2002 http://www.iee.org/Publish/Digests/conf2002.cfm See IEE Proceedings, Radar, Sonar and Navigation Web link http://ioj.iee.org.uk/journals/ip-rsn See Edinburgh MD96 - Detection of abandoned landmines (Main Past Conference) Web link: http://www.iee.org/Publish/Digests/confl996.cfm See Edinburgh MD98 - Second International Conference on the Detection of Abandoned Land Mines (Main Past Conference) Web link: http://www.iee.org/Publish/ Digests/confl998.cfm 1.5.5
Institute of Electrical and Electronics Engineers (USA)
Proceedings - particularly the Societies for: Antennas and Propagation http: //www. ieeeap s. org/ Aerospace and Electronic Systems http://ewh.ieee.org/soc/aes/ For Radar conferences see also http://www.ewh.ieee.org/soc/aes/Conferences.html Geoscience and Remote Sensing http://www.ewh.ieee.org/soc/grss/ Microwave Theory and Transactions http ://www.mtt. org/ 1.5.6
SPIE (International Society for Optical Engineering)
conferences
SPIE Orlando: SPIE Detection and Remediation Technologies for Mines and Minelike Targets 1995 to 2003 http://spie.org/app/conferences/index.cfm?fuseaction=archive&year=2002
1.5.7 Geophysics http://www.geo-online.org/ 1.5.8 Sub-surface sensing technologies and applications http://www.kluweronline.eom/issn/l 566-0184
1.6
References
[1] SKOLNIK, M. L: 'An introduction to impulse radar'. Naval Research Laboratory Report 6755, November 1990 [2] DANIELS, D. J., GUNTON, D. J., SCOTT, H. R: 'Introduction to subsurface mdar\ IEE Proc.-F, Commun. Radar Signal Process., 1988,135, pp. 278-320 [3] HULSENBECK et al.: German Pat. No. 489434, 1926 [4] STEENSON, B. 0.: 'Radar methods for the exploration of glaciers'. PhD Thesis, Calif. Inst. Tech., Pasadena, CA, USA, 1951 [5] EVANS, S.: 'Radio techniques for the measurement of ice thickness', Polar Record, 1963,11, pp. 406-410 [6] UNTERBERGER, R. R.: 'Radar and sonar probing of salt'. 5th Int. Symp. on Salt, Hamburg (Northern Ohio Geological Society), pp. 423-437 [7] KADABA, P. K.: 'Penetration of 0.1 GHz to 1.5 GHz electromagnetic waves into the earth surface for remote sensing applications'. Proc. IEEE S. E. Region 3Conf, 1976, pp. 48-50 [8] MOREY, R. M.: 'Continuous sub-surface profiling by impulse radar'. Proc. Conf. Subsurface Exploration for Underground Excavation and Heavy Construction. Am. Soc. Civ. Eng., 1974, pp. 213-232 [9] COOK, J. C : 'Status of ground-probing radar and some recent experience'. Proc. Conf. Subsurface Exploration for Underground Excavation and Heavy Construction. Am. Soc. Civ. Eng., 1974, pp. 175-194 [10] COOK, J. C : 'Radar transparencies of mine and tunnel rocks', Geophys., 1975, 40, pp. 865-885 [11] ROE, K. C , ELLERBRUCH, D. A.: 'Development and testing of a microwave system to measure coal layer thickness up to 25 cm'. Nat. Bur. Stds., Report No.SR-723-8-79 (Boulder, CO), 1979 [12] NILSSON, B.: 'Two topics in electromagnetic radiation field prospecting'. Doctoral Thesis, University of Lulea, Sweden, 1978
Chapter 2
System design
2.1
Introduction
GPR has an enormously wide range of applications, ranging from planetary exploration to the detection of buried mines. The selection of a range of frequency operations, a particular modulation scheme, and the type of antenna and its polarisation depends on a number of factors, including the size and shape of the target, the transmission properties of the intervening medium, and the operational requirements defined by the economics of the survey operation, as well as the characteristics of the surface. The specification of a particular type of system can be prepared by examining the various factors which influence detectivity and resolution. To operate successfully, ground penetrating radar must achieve: (a) (b) (c) (d)
an adequate an adequate an adequate an adequate
signal to clutter ratio signal to noise ratio spatial resolution of the target depth resolution of the target.
Most GPR systems detect the backscattered signal from the target, although forward transmission methods are used in borehole tomographic radar imaging. This Chapter considers the principal factors affecting the design of a GPR in order to illustrate those factors which need to be considered. The aim is to illustrate the technical options available to the operator or designer. This is not a rigorous treatment of radar system analysis but does enable an order of magnitude estimate of the various loss components to be assessed. Many radar systems generate a fast rise time impulsive voltage, so the signal level is best considered from the point of view of voltages across particular nodes in the network. A consideration of this approach is given at the end of this section, and an expression suitable for evaluation using MathCAD™ is included, together with a series of modelled results for particular values. A block diagram of a generic radar system is shown in Figure 2.1. The source of energy can be an amplitude, frequency or phase modulated waveform or noise signal, and the selection of the bandwidth, repetition rate and mean power will depend upon
transmitter
Figure 2.1
receiver
processor
display
Block diagram of generic radar system
the path loss and target dimensions. The transmit and receive antennas will usually be identical and will be selected to meet the characteristics of the generated waveform. The receiver must be suitable for the type of modulation and down-conversion and possess an adequate dynamic range for the path losses that will be encountered. The various design options are shown in Figure 2.2, and will be discussed in Section 2.7 as well as in subsequent chapters. An initial estimate of the range performance of the radar can be gained by considering the following factors: path loss, target reflectivity, clutter and system dynamic range. The spatial resolution of the radar can be determined by considering the depth and plan resolution separately. The majority of GPR systems use an impulse time domain waveform and receive the reflected signal in a sampling receiver. However, more use has been made of FMCW and stepped frequency radar modulation schemes in recent years and, as the cost of the components decreases, it may be expected that more of these systems will be used, as their dynamic range can be designed to be greater than the time domain radar.
2.2
Range
2.2.1 Introduction The range of a GPR is primarily governed by the total path loss, and the three main contributions to this are the material loss, the spreading loss and the target reflection loss or scattering loss.
radar system design options
domain
time
modulation
amplitude
linear sweep
matched filter direct sampling sequential sampling
receiver
spatial
frequecy
stepped frequency
pseudorandom
holographic (single frequency)
complex I/Q mixer correlator
down-conversion
processing
Figure 2.2
singularity expansion methods wavelet transforms
image processing
pattern recognition neural networks
Ground penetrating radar system design options
An example of a simplified general method of estimation is given in this section. It should be noted that this contains many simplifying assumptions, which later chapters will discuss in more detail. The main assumption relates to the spreading loss. In conventional free-space radar the target is in the far field of the antenna and spreading loss is proportional to the inverse fourth power of distance provided that the target is a point source. In many situations relating to ground penetrating radar the target is in the near field and Fresnel zone and the relationship is no longer valid. However, for this example an R~4 spreading loss will be assumed, even though for a planar interface this is not valid and a correction is included. The signal that is detected by the receiver undergoes various losses in its propagation path from the transmitter to the receiver (see Figure 2.3). The total path loss for a particular distance is given by (2.1)
transmit antenna
breakthrough
receive antenna
sidelobe clutter interface reflection
front surface reflection ground clutter
2nd layer I anomaly
Figure 2.3
Physical layout of radar system
material 1
material 2
Figure 2.4
Outline arrangement of GPR system
where: antenna efficiency loss in dB antenna mismatch losses in dB transmission loss from air to material in dB retransmission loss from material to air in dB antenna spreading losses in dB attenuation loss of material in dB target scattering loss in dB
At a fixed frequency of, say, 100 MHz these losses may be estimated. In general, for accurate prediction, this calculation needs to be made over a wide band of frequencies, but for this example a single frequency is assumed. The radar to be considered is an impulse radar using planar loaded dipole antennas operated on the ground surface and the target is a planar interface at a depth of LOm from the front surface of the material as shown in Figure 2.4. For this example, the lateral dimensions of the planar interface can be considered to be infinitely large. The example will assume that for the first layer of soil er — 9 and tan 5 = 0.1 while for the second layer of soil er — 16 and tan 8 = 0.5. This gives the modulus of impedance of the first layer as 125 Q and the second as 89 Q at a frequency of 100 MHz.
2.2.2 Antenna loss The antenna efficiency is a measure of the power available for radiation as a proportion of the power applied to the antenna terminals. In the case of resistively loaded antennas the efficiency is not high and is the result of the need for wideband operation. It would be expected that over an octave bandwidth the efficiency of a loaded antenna would be 4 dB lower than that of an unloaded antenna, which might have a loss of 2 dB. For other types of antenna, i.e. the short axial horn, TEM horn, etc., the antenna efficiency is higher and lower losses can be expected. In the example under consideration it is assumed that Le = — 2 dB per antenna, i.e. —4 dB for a pair of loaded dipole antennas.
2.2.3 Antenna mismatch loss The antenna mismatch loss is a measure of how well the antenna is matched to the transmitter; usually little power is lost by reflection from antenna mismatch and is in the order of— 1 dB. 2.2.4
Transmission coupling loss
In the case of antennas operated on the surface of the material the transmission loss from the antenna to the material is given by (2.2) where: Za = characteristic impedance of air, which equals 377 Q Zm = characteristic impedance of the material, (2.3) Typically, for many earth materials Zn, = 125 Q; hence L,\ = —2.5 dB.
2.2.5 Retransmission coupling loss The retransmission loss from the material to the air on the return journey is given by (2.4)
2.2.6 Spreading loss The antenna spreading loss is conventionally related to the inverse fourth power of distance for a point reflector, and in this example the ratio of the received power to the transmitted power is given by (2.5)
where: gain of transmitting antenna (loaded dipole) = 1 5 receiving aperture (loaded dipole) = 4 x 10~2 m2 range to the target = LOm radar cross-section (a = Im 2 ). Hence Ls can be defined as
(2.6) It should be noted that the radar range equation assumes a point source scatterer, which is not always the case. The range law may need adjusting for the different types of targets as shown in Table 2.1, and in this case a planar relationship is used. The nature of the target influences the magnitude of the received signal. The following approximate relationships apply for targets, which extend across the zone illuminated by an antenna (i.e. its footprint). Considerably more backscattered energy will be returned from a planar reflector at a given depth compared with other target types exhibiting similar dielectric contrasts. As the target assumed in this example is a planar interface, a correction to the R~4 law is necessary.
Table 2.1 Adjustment of range law for different types of target Nature of target
Magnitude of received signal
Point scatterer (small void) Line reflector (pipeline) Planar reflector (smooth interface)
(target depth)" 4 (target depth)" ^ (target depth)" 2
2.2.7 Target scattering loss In the case of an interface between the material and a plane, where both the lateral dimensions of the interface and the overburden are large, then (2.7) Z\ = characteristic impedance of first layer of material Z2 = characteristic impedance of second layer of material 0 = target radar cross-section Note that the radar cross-section should be considered as a bistatic radar cross-section in relation to the antenna radiation patterns. Typically, Lsc would be in the order of — 1.6dB for the interface between the first and second layers. In this example 0 is considered to be unity, i.e. 0 dB, as the situation is equivalent to an infinite dielectric half-space. Where the physical dimensions of the interface or anomaly are small, then the target scattering loss Lsc increases due to the geometry of the situation, and the returned signal becomes smaller. Under some conditions the physical dimensions of the anomaly are such as to create a resonant structure, which increases the level of the return signal and decreases the target scattering loss. It is possible to distinguish air filled voids and water filled voids by examination of their resonant characteristics and the relative phase of the reflected wavelet. Water has a relative dielectric constant of 81, which will serve to reduce the resonant frequency of any void by a factor of 9 C N / ^ ) , and this variation may be the means of identifying water filled voids. Table 2.2 gives an indication of the radar cross-sectional area in free space. The dimensions should be corrected for the different wavelengths within the material. The following radar cross-sections are, of course, relevant only to extended scatterers, and this should be taken into account when calculating overall system losses. Many of the targets being searched for by sub-surface radar methods are nonmetallic, so their scattering cross-section is dependent upon the properties of the surrounding dielectric medium. Where the relative permittivity of the target is lower than that of the surrounding medium, such as an air-filled void below a concrete ground slab, the interface does not produce a phase reversal of the backscattered
Table 2.2 Scatterer
Radar cross-sections Aspect
Radar CSA
Sphere
Symbols a — radius
Flat plate arbitrary shape
Normal
A — plate area
Cylinder
Angle broadside
a — radius / = length
Prolate spheroid
Axial
#0 = major axis bo = minor axis
Triangular trihedral corner reflector
Symmetry axis
L = side length
wave. Conversely, when the scattering is caused by a metallic boundary or where the relative permittivity of the target is larger than that of the surrounding medium, phase reversal occurs in the backscattered wave. This phenomenon may be used as a way of distinguishing between conducting and nonconducting targets. The physical shape of the target will influence the frequency and polarisation of the backscattered wave and can be used as a means of preferential detection. The effect of the high permittivity of typical soil means that some targets, such as thin-walled plastic pipes, produce a stronger radar return when buried than when in free space. In such circumstances, the radar is responding primarily to the dielectric properties of the enclosed volume (i.e. the water or air-filled space within the pipe). The type of target being sought (i.e. a sphere, a linear target such as a pipe or an interface) affects the choice of antenna type and configuration as well as the kind of signal processing techniques which may be employed. Generally, parallel arrangements of dipole antennas are suitable for most targets whereas crossed dipoles are more appropriate for either small or linear targets.
2.2.8 Material attenuation loss The attenuation loss of the material is given by
(2.8)
Table 2.3 Material
Material loss at 1OO MHz and 1 GHz Loss at 100 MHz Loss at 1 GHz
Clay (moist) 5-300 dB m" 1 Loamy soil (moist) 1-60 dB m~l Sand (dry) 0.01^dBm" 1 Ice O.^dBm"1 Fresh water 0.1 dB m~l Sea water 10OdBm"1 Concrete (dry) 0.5-2.5 dB m~* Brick 0.3-2.OdBm"1
50-3000 dB m" 1 10-600 dB m~1 0.1-2OdBm"1 1-5OdBm"1 1 dB m~l 100OdBm"1 5-25 dB m~l 3-2OdBm"1
where: frequency in Hz loss tangent of material relative permittivity of material absolute permittivity of free space relative magnetic susceptibility of material absolute magnetic susceptibility of free space Atypical range of loss for various materials at 100 MHz and 1 GHz is shown in Table 2.3.
2.2.9 Total losses From the previous sections the total losses that will occur at 100 MHz during transmission through 1 m of material of 2.7 dB/m attenuation and then reflection from a boundary interface, where Z\ = 125 Q and Z^ = 89 £2 would be
(2.9) A basic model for this situation using Mathcad™ is given on the CD, and parameters can be changed to model different situations. On the CD click onto Gpr-signalrange.mcd to view the sheet. Change the parameter values for er and tan S to see the effect of material changes. A plot of the various components of the returned signal is given in Figure 2.5. In the case of a time domain radar system it is more practical to consider peak voltages. The capability of a sub-surface radar system to detect a reflected signal of peak voltage Vr, if the peak transmitted voltage is Vt, can be termed the detectability
Ref
signal level, dB
Lref LspreadR LattenR detect LclutterR
range R, m reference fixed losses spreading loss attenuation noise floor clutter
Figure 2.5
Signal amplitude against range
of the radar system,
The limiting factor of detectability is the noise performance of the receiver; hence the received voltage must be greater than the noise voltage generated by the latter. In the case of the previously calculated loss, if the transmitter generates a pulse of peak magnitude 50 V, then the peak received signal would be 112 mV. Most time domain radar receivers can detect a 1 mV signal even without averaging; hence a reflected wavelet of peak amplitude of 112mV should be capable of being easily detected. This is only the case if the clutter signals are also low and the amplitude of the clutter signal should also be determined at the same range. Figure 2.5 shows a graph of the various signal levels plotted against range over the interval 1 to 10 m. Note that close to the antenna that is in the range 0 to 1 m, the above analysis is not applicable. From the values of attenuation indicated above and the nature of the frequency dependence, it follows that for a given signal detection threshold the maximum depth of investigation decreases rapidly with increasing frequency. Most sub-surface radar systems operate at frequencies less than 2 GHz. Figure 2.6 shows for a range of materials measured by Cook [1] the maximum depth of penetration at which radar is likely to be able to give useful information and the approximate upper frequency of operation. Typical maximum depths of penetration rarely exceed 20 wavelengths, except in very low attenuation dielectric mediums. Often the depths of penetration will be much less, particularly in lossy dielectrics.
radar performance figures (PF) upper curves = 150 dB lower curves = 100 dB
Medium
Data source (table)
frequency ( / ) , MHz
Figure 2.6
Radar probing range (after Cook [I])
It might be thought that a GPR needs to have as low a frequency of operation as possible to achieve adequate penetration in wet materials. However, the ability to resolve the details of a target or separately detect two targets is proportional to the size or spacing of the target in relation to the wavelength of the incident radiation. Consequently a high frequency is desirable for resolution. A compromise between penetration and resolution must be made and is an important consideration in either the selection of system bandwidth or the range of frequencies to be radiated. Consideration needs also to be given to the fact that, not only does attenuation decrease with frequency, but so does target scattering cross-section. This leads to the situation where it is possible that, for certain targets, material properties and depths, the received signal decreases with frequency. This effect is shown in Figure 2.7 (from Daniels et al. [2]), where the ratio between the reflected power, at frequencies of 50 MHz and 500 MHz, at the ground surface has been calculated for small diameter metallic (broken line) or nonmetallic (solid line) cylinders. In addition to the estimation of signal levels, it is possible to determine the probability of detection and the probability of false alarm for a particular target, and this is shown in Section 3.2.
MB
burial depth, m
soil loss, dBnr 1 at 5^0MHz
Figure 2.7
2.3
Received signal level of various targets (after Daniels et ah [2])
Velocity of propagation
It can easily be recognised that if the propagation velocity can be measured, or derived, an absolute measurement of depth or thickness can be made. For homogeneous and isotropic materials, the relative propagation velocity can be calculated from (2.10) and the depth derived from (2.11) where er is the relative permittivity and t is the transit time to and from the target. In most practical trial situations the relative permittivity will be unknown. The velocity of propagation must be measured in situ, estimated by means of direct measurement of the depth to a physical interface or target (i.e. by trial holing), or by calculation by means of multiple measurements. From Figure 2.8 it can be seen that if a hyperbolic spreading function can be measured then the propagation velocity can be derived from (2.12) and the depth to the target (2.13)
Figure 2.8
Hyperbolic spreading function
ground surface
planar interface
depth
Figure 2.9
Common depth point estimation
An alternative method of calculating the depth of a single planar reflector is by means of the common depth point method. If both transmitting and receiving antennas are moved equal distances from the common centre point the same apparent reflection position will be maintained. The depth of the planar reflector can be
derived from (2.14) where the two positions of the antenna are shown in Figure 2.9. The variation of permittivity with frequency in wet dielectrics implies that there will be some variation in the velocity of propagation with frequency. The magnitude of this effect will generally be small for the range of frequencies typically employed for sub-surface radar work. A dielectric exhibiting this characteristic is said to be 'dispersive'. Where the material has different propagation characteristics in different Table 2.4
Material propagation characteristics
Material
Relative permittivity
Air Concrete Freshwater
1 9 80
Propagation velocity, cm/ns
30 10 3.35
Wavelength 100 MHz cm
IGHz cm
300 100 33
30 10 3
kjk
relative permittivity
Figure 2.10
Normalised wavelength against relative permittivity
directions it is said to be anisotropic, and an example is coal in the seams prior to excavation, where the propagation characteristics normal to the bedding plane are different from those parallel to the plane. In free space the propagation velocity, c, is 3 x 108 ms" 1 . The velocity in air is very similar to that in free space and is normally taken as the same. In sub-surface radar work the elapsed time between the transmitted and received pulses is measured in nanoseconds (10~9 s) because of the short travel path lengths involved. Propagation velocity decreases with increasing relative permittivity. The wavelength within the material also decreases as the velocity of propagation slows in accordance with the following relationship: wavelength
(2.15)
The result of these effects is illustrated by Table 2.4; see also Figure 2.10.
2.4
Clutter
The clutter that affects a GPR can be defined as those signals that are unrelated to the target scattering characteristics but occur in the same sample time window and have similar spectral characteristics to the target wavelet. This is a somewhat different definition from conventional radar clutter and should be borne in mind when considering conventional methods of clutter filtering such as MTI, which would be inappropriate to apply to ground penetrating radar data. Clutter can be caused by breakthrough between the transmit and receive antennas as well as multiple reflections between the antenna and the ground surface. Clutter will vary according to the type of antenna configuration, and the parallel planar dipole arrangement is one where the stability of the level of breakthrough is most constant. Typically a maximum level of —40 dB to —50 dB is encountered. The planar crossed dipole antenna can be designed and manufactured to provide very low levels of breakthrough (>70dB). However, it then becomes very susceptible to 'bridging' by dielectric anomalies on the near surface which can degrade the breakthrough in a random manner as the antenna is moved over the ground surface. The variability of the breakthrough is unfortunate as it is not usually amenable to signal processing. The same problem is encountered with planar spiral antennas. Local variations in the characteristic impedance of the ground can also cause clutter, as can inclusions of groups of small reflection sources within the material. In addition, reflections from targets in the side lobes of the antenna, often above the ground surface, can be particularly troublesome. This problem can be overcome by careful antenna design and incorporating radar absorbing material to attenuate the side and back lobe radiation from the antenna. In general, clutter is more significant at short range times and decreases at longer times. It is possible to quantify the rate of change of the peak clutter signal level as a function of time as in many cases this parameter sets a limit to the detection capability
of the radar system. The effect of clutter on system performance is shown in Figure 2.5, which illustrates the consequent limitation on near-range radar performance. Various techniques have been investigated in the search for a method of reducing clutter. In the case of impulse radars using TEM horns or FMCW radars using ridged horns and reflectors, it has been found possible to angle the bore sight of the horn antennas to take advantage of the critical angle, thereby suppressing to some extent the ground surface reflection.
2.5
Depth resolution
There are some applications of sub-surface radar, such as road layer thickness measurement, where the feature of interest is a single interface. Under such circumstances it is possible to determine the depth sufficiently accurately by measuring the elapsed time between the leading edge of the received wavelet and a reference time such as the front surface reflection provided the propagation velocity is accurately known. However, when a number of features may be present, such as in the detection of buried pipes and cables, then a signal having a larger bandwidth is required to be able to distinguish between the various targets and to show the detailed structure of a target. In this context it is the bandwidth of the received signal which is important, rather than that of the transmitted wavelet. The 'earth' acts as a lowpass filter, which modifies the transmitted spectrum in accordance with the electrical properties of the propagating medium. The results from a simplified model of this situation are shown in Figure 2.11, where the general pulse stretching can be seen for different rates of attenuation. A Ricker wavelet has been used as the source impulse as this is a typical impulse. Note that the output impulse has been auto-scaled for clarity and actually is severely attenuated as the lowpass filter slope is increased. The required receiver bandwidth B' can be determined by considering the power spectrum of the received signal. The power spectrum results from the Fourier transform of the received signal wavelet. If the envelope of the wavelet function is considered, it is possible from the Rayleigh criterion for resolution to determine the receiver bandwidth. An alternative definition of the receiver bandwidth is given by Cook [1] and is derived from the autocorrelation function of the signal wavelet. If f(t) is the wavelet, then the autocorrelation function is given by (2.16) The general shape of the autocorrelation function shown in Figure 2.12, which is related to the matched filtering resolution, can be used to define the bandwidth requirement. The autocorrelation function is, of course, related to the power spectrum of the received waveform and is therefore a useful measure. A receiver bandwidth in excess of 500 MHz and typically 1 GHz is required to provide a typical resolution of between 5 and 20 cm, depending on the relative permittivity of the material.
The required receiver bandwidth can be determined by considering the power spectrum of the received signal. The power spectrum results from the Fourier transform of the received signal wavelet and is shown in Figure 2.13. If the envelope of the wavelet function is considered as shown in Figure 2.14, then it is possible from the Rayleigh criteria for resolution to determine a receiver bandwidth. An alternative definition of the receiver bandwidth is given in Reference [1] and is derived from the autocorrelation function of the signal wavelet.
amplitude, V
a
result (t) input (t)
time / in arbitrary units 7.5 dB per octave attenuation
amplitude, V
b
result (t) input (t)
time t in arbitrary units 15 dB per octave attenuation
Figure 2.11
Effect of ground attenuation on pulse length
amplitude, V
C
result (0 input (0
t time t in arbitrary units 30 dB per octave attenuation
amplitude, V
d
result (0 input (/)
t time t in arbitrary units 60 dB per octave attenuation
Figure 2.11
Continued
Although a greater depth resolution is achieved in wetter materials for a given transmitted bandwidth, earth materials with significant water content tend to have higher attenuation properties. This characteristic reduces the effective bandwidth, tending to balance out the change so that within certain bounds the resolution is approximately independent of loss within the propagating material. Where interfaces are spaced more closely than one half wavelength the reflected signal from one interface will become combined with that from the other, as shown
amplitude, V
Ricker (O result (/)
time t in arbitrary units
amplitude, V
Figure 2.12
A utocorrelation of wavelet function
amp (/)
frequency / in arbitrary units
Figure 2.13
JV 32
Spectrum of autocorrelation function of Ricker wavelet
amplitude, arbitrary units
envelope of autocorrelation
env (0 -env (0 result (0
N time / in arbitrary units
Figure 2.14
Envelope of autocorrelation function of Ricker wavelet
infinite resolution
composite reflection
1st interface 2nd interface
3rd interface
4th interface
time
Figure 2.15
time
time
time
time
time
Convolution of multiple interface reflections
in Figure 2.15. In such circumstances some form of deconvolution processing would be required in order to recognise the responses from the individual interfaces and to enable them to be characterised and traced. However, such processing is not normally carried out during standard commercial radar surveys.
2.6
Plan resolution
The plan resolution of a subsurface radar system is important when localised targets are sought and when there is a need to distinguish between more than one at the same depth. Where the requirement is for location accuracy, which is primarily a topographic surveying function, the system requirement is less demanding. The effect of the radiation footprint on the ground can be seen from Figure 2.16, where the distance between the radiating source and the ground surface has been increased from 0.1 m to 0.5 m (left to right). The ground area is 2 m by 2 m and it can be seen that the width of the 3 dB footprint increases considerably as the source is raised from the ground. The effect of this on the image resolution is also considerable as the convolution of the antenna pattern with the target causes a blurring of the target image as shown in Figure 2.17. The plan resolution is defined by the characteristics of the antenna and the signal processing employed. In general, to achieve an acceptable plan resolution requires a high gain antenna. This necessitates an antenna with a significant aperture at the lowest frequency transmitted. To achieve small antenna dimensions and high gain therefore requires the use of a high carrier frequency, which may not penetrate the material to sufficient depth. When choosing equipment for a particular application it is necessary to compromise between plan resolution, size of antenna, the scope for signal processing and the ability to penetrate the material.
Figure 2.16 a
Figure 2.17
Radiation footprint on the ground from an isotropic source b
Effect of convolution of antenna footprint on radar image
Plan resolution improves as attenuation increases, assuming that there is sufficient signal to discriminate under the prevailing clutter conditions. In low attenuation media the resolution obtained by the horizontal scanning technique is degraded, but under these conditions the use of advanced signal processing techniques becomes feasible. These techniques typically require measurements made using transmitter and receiver pairs at a number of antenna positions to generate a synthetic aperture or focus the image. Unlike conventional radars, which generally use a single antenna, most GPR systems use separate transmit and receive antennas in what has been termed a bistatic mode. However, as the antenna configuration is normally mobile, the term bistatic is not really relevant. The descriptions normally applied to the modes of geophysical survey appear more relevant and are therefore introduced. Geophysicists classify surveys in four main modes: common source, common receiver, common offset and common depth point, as shown in Figure 2.18. Most GPR surveys use a common offset survey mode in which the separation between the transmitter and receiver is fixed. However, both common depth point and common source or receiver modes have also been used but require different signal processing approaches. In the common offset mode the transmitter and receiver antennas are scanned above the ground surface over a buried target as shown in Figure 2.18. The received
ground surface
planar interface common source
ground surface
planar interface common offset
ground surface
planar interface common depth point
ground surface
planar interface common receiver
Figure 2.18
Geophysical survey modes
power for a point source scatterer in the far field can be shown to be proportional to (2.17) where a is the attenuation coefficient and 0 is the angle between the midpoint of the combined transmit-receive antenna and the vertical to the target. Where the plan resolution is defined as the half power points of the spatial response of the scatterer at the plane of the surface, the resolution is approximated by (2.18) This approximation takes no account of the antenna beam pattern in either x or y directions. However, it does indicate that as the attenuation increases the plan resolution improves, provided that adequate signal to noise and signal to clutter ratios are maintained. It should be noted that, in low attenuation materials, synthetic aperture processing can be applied and plan resolution is recovered. Typically the improvement in resolution is most noticeable at depths greater than 1 m, and an improvement in resolution of 30% would be found in the plan resolution of targets buried at 2 m in materials of 9 dB m" 1 and 30 dB m" 1 attenuation.
2.7
System considerations
The majority of surface penetrating radars are based on the time domain impulse design. Alternative design options can be considered, and experimental versions of stepped frequency (SFCW) or synthesised impulse (SI), as well as frequency modulated (FMCW), noise or pseudo random coded (PRC), have been designed and built. While the different modulation techniques are considered in detail in Chapter 6 it is useful to summarise the general attributes of each option (see Figure 2.19). Time domain impulse radar systems are available commercially, and manufacturers usually offer a range of antennas and pulse lengths to suit the desired probing range. Depths of greater than 30 m require pulse lengths in the order of 40 ns (approximately a bandwidth of 50 MHz at a centre frequency of 25 MHz), and very short range precision probing may use pulse lengths of the order of or less than 1.0 ns that is, an approximate bandwidth of 2 GHz at a centre frequency of 1 GHz. Planar impulse radar antennas generally operate closely coupled to the ground and are usually designed so that the polarisation of the transmitted and received signals are parallel. The exception to this is the crossed dipole antenna, which has been used for detecting either linear features such as pipes, cables and cracks in the material or small targets such as buried plastic mines. Most antennas have a relatively small footprint, which means that rapid and wide area surveying can only be achieved with multi-channel radar systems. For road survey such methods are cost effective and practical. An alternative to the planar antenna is the TEM horn, which can be used with a surface to antenna spacing of up to 1 m.
co-ordinate system
antenna design
operational requirements
hardware design
storage requirements
target properties
signal processing
image presentation
material properties
Figure 2.19
System design considerations
Although alternative modulation methods to the impulse radar have been used, there is very little commercially available FMCW, stepped frequency or synthesised pulse radar equipment, although this situation could change in the future. Whatever system is considered it is important to consider the receiver dynamic range and sensitivity rather than the ratio of the peak transmitted signal to the minimum detectable signal. A practical example will illustrate the reason for this. If a GPR is being used to survey the road and traverses a metal cover on the surface of the road the received signal will be maximum and may well saturate the receiver circuits. If the receiver cannot recover from this high level input within a few nanoseconds, all low level signals caused by targets deeper than and adjacent to the cover will go undetected. It is therefore the receiver performance and the method of signal down-conversion which must be considered as defining the overall performance. A receiver with a true dynamic range of 60 dB followed by an analogue to digital converter with a dynamic range of 96 dB (16 bits) is only capable of providing an effective dynamic range of 60 dB. Great care should be taken when interpreting specifications to ascertain the true system performance.
2.8
References
[1] COOK, J.: 'Radar transparencies of mine and tunnel rocks', Geophysics, 1975, 40, (5), pp. 865-885 [2] DANIELS, D. J., GUNTON, D. J., SCOTT, H. R: 'Introduction to sub-surface radar', IEE Proceedings F, 1988,135, (4), pp. 278-321
Chapter 3
Modelling techniques
3.1
Introduction
Models of the GPR situation range from a simple single frequency evaluation of path losses to complete 3D time domain descriptions of the GPR and its environment. This Chapter introduces some of the approaches and provides a starting point for further exploration of the literature. Modelling techniques include single frequency models, time domain models, ray tracing, integral techniques (MOM - method of moments) and discrete element methods. The finite-difference time-domain (FDTD) technique has become one of the popular techniques and can be developed to run on most desktop computers with relative efficiency. The most basic model uses the radar range equation and enables an estimate of received signal level, dynamic range and probability of detection to be assessed. It has significant weaknesses in that most close range GPR systems are operating in the near field or even the reactive field of the antenna (which is also in a bistatic mode), whereas the model assumes a far field model. It is probably more relevant to the longer-range geophysical applications where the target is many tens of metres from the radar. This is described in Section 3.2. A transmission line model, which enables an A-scan representation to be generated, is described in Section 3.3 and is followed by a simulation using a finite-difference time domain (FDTD) method to model the field propagation of a typical GPR system. Sections 3.4 and 3.5 provide further and more detailed examples of modelling methods as applied to particular situations. Other models are available from academic sources or as commercial products from vendors of GPR equipment and geophysical houses. Work on the modelling of GPR antennas has been carried out by Huang etal. [1], Lee et al [2] and Guangyou et al [3] using an FDTD method, as well as by Martel et al [4] and Meincke and Kim [5]. Particular attention has been paid to soil effects by Teixeira et al [6, 7], Chew et al [8], Oguz and Gurel [9], Liu and Fan [10],
Liu et al. [11], Rappaport and Weedon [12], and Gurel and Oguz [13]. Special consideration to rough surfaces has been made by Rappaport and El-Shenawee [14]. Three-dimensional modelling of GPR has been carried out by Zhan et al. [15], Gurel and Oguz [16], and Oguz and Gurel [17]. Further modelling techniques are explored by Desai et al. [18] and Wang et al. [19], who carried out a SAR simulation. GprMax2D Vl.5 (electromagnetic simulator for ground-probing radar) is freely available for teaching and research purposes and can be downloaded in either Windows™ or Linux (http://www.gprmax.org/) and was developed by Dr Antonis Giannopoulos of the University of Edinburgh. Modelling programmes are also available from Dr Gary Olhoeft from his website at http://www.g-p-r.com/, while commercial products are also available from http://www.ka.shuttle.de/software/ Reflex/gpr.htm.
3.2
Received signal levels and probability of detection
The most basic model for assessment of signal level is derived from the radar range equation, which does, however, have severe limitations with respect to correct representation of the actual operation of a short range ( er\, such as where an air-filled void exists in a dielectric material. The effect on a pulse waveform is to change the phase of the reflected wavelet so that targets with different relative dielectric constants to the host material show different phase patterns of the reflected signal. However, the amplitude of the reflected signal is affected by the propagation dielectric of the host material, the geometric characteristics of the target and its dielectric parameters, as indicated in Figure 4.6. Figures 4.7 and 4.8 show the predicted relative received signal at frequencies of 100 MHz and 1 GHz for a planar interface, where the first layer relative dielectric constant is 4. The second layer relative dielectric constant is 16 and has a loss tangent of0.05. The previous description is an elementary description of a situation, which is described with considerably more precision by Wait [3] and King et al. [4]. Wait initially considers the one-dimensional case of propagation of a transient field in a homogeneous infinite medium with conductivity a, dielectric constant s and permeability /x. Wait's general method is to determine the form of the magnetic and electric fields at a distance from the source point. The transient fields are represented as Fourier integrals and, in the case where the driving function is a unit impulse, the time domain characteristics of the far field response are derived. Wait further develops the general approach for the case of a dipole on a dielectric half-space and concludes that the main feature of propagation in conducting media is that the waveform changes its shape as it propagates away from the source. As a consequence resolution is severely degraded. However, this loss of fidelity could also be used as an indicator of distance travelled. King and Wu [4] treat the situation of the propagation of a radar pulse in sea water in similar general manner and draw a parallel to the treatment by Brillouin [5] and Sommerfeld [6] of the propagation of optical pulses in a linear, causally dispersive medium and in an updated form by Oughstrun [7]. King considers analytically the case of the near field generated by the rectangular pulse modulated current in an
signal level, dB
range R, m reference
Figure 4.7
Received signal level against range at 1OO MHz Tan 5 = 2.1 x 10~3, 1.05 x 1(T2, 1.7 x 1(T2, 2.4 x 1(T2 and2.9 x 1(T2
electric dipole in sea water. This situation is a useful model for pulse propagation in a dissipative and dispersive medium from a dipole source. King concludes that the amplitude of the wave packet decays more rapidly than the amplitudes of the transient components. Finkelshteyn and Kraynyukov [8] also consider the effect of the medium on pulse propagation characteristics. Wait and Nabulsi [9] also consider the possibility of preforming the pulse shape to suit particular lossy media.
4.3
Properties of lossy dielectric materials
The electromagnetic behaviour of natural and man-made materials is generally complicated because all exhibit both dielectric and conducting properties. Their electromagnetic characteristics are controlled by the microscopic scale (atomic, molecular and granular) behaviour of the components making up the materials. The origins of various dielectric losses as a function of frequencies are shown schematically in Figure 4.9. The effects occur at different frequencies, which creates a frequency dependency in the dielectric properties of these materials. Figure 4.10 illustrates the changes which take place in the relative permittivity, and the dielectric loss factor, over an extremely
signal level, dB
range R, m reference
Figure 4.8
Received signal level against range at 1 GHz Tan 8 = 2.1 x 1(T6, 1.05 x 1(T5, 1.9 x 1(T5, 2.7 x 10" 5 and 3.6 x 1(T5 water relaxation ice, relaxation
a
Maxwell/Wagner losses conductivity
JC
crystal water bound forms of water, relaxation b relaxation surface
x
charged double conductivity layers
log frequency
Figure 4.9
Origin of dielectric losses in heterogeneous materials containing water (after De Loor [W])
complex relative permittivity
log frequency, Hz
Figure 4.10
Schematic diagram of the complex relative permittivity relaxation region (atomic and electronic resonance regions) sr = e'r — je"
wide frequency range. In this idealised representation the relative permittivity effectively remains constant at high and low frequencies. However, there is a transition region over an intermediate frequency band where the dielectric properties change significantly with frequency. This region is of particular interest when it occurs in the microwave band. In the regions of electronic resonance (~10 15 Hz) occur at frequencies far higher than those associated with surface-penetrating radar. Therefore they need not be considered any further in relation to the frequency range of interest. The relaxation phenomenon portrayed relates to the disturbance ofpolar molecules by an impressed electric field, each molecule experiencing a force that acts to orientate the permanent dipole moment characteristic of the molecule parallel to the direction of the applied electric field. This force is opposed by thermodynamic forces. If an alternating electric field is applied, the individual molecules will be induced to rotate in an oscillatory manner about an axis through their centres, the inertia of the molecules preventing them from responding instantaneously. Similar translational effects can occur. The polarisation produced by an applied field (such as a propagating radar wave) is closely related to the thermal mobility of the molecules and is, therefore, strongly temperature dependent. In general, the relaxation time (which may be expressed as a relaxation frequency) depends on activation energy, the natural frequency of oscillation of the polarised particles, and on temperature. Relaxation frequencies vary widely between different materials. For example, maximum absorption occurs at very low frequencies in ice (103 Hz), whereas it takes place in the microwave region in water (106 — 10 10 Hz). Thus the effects of this phenomenon could have a direct bearing upon the dielectric properties of materials at the frequencies employed by surfacepenetrating radars, especially if moisture is present within a material. There are a number of other mechanisms, which cause a separation of positively and negatively charged ions resulting in electric polarisation. These mechanisms can be associated with ionic atmospheres surrounding colloidal particles (particularly clay minerals), absorbed water and pore effects, as well as interfacial phenomena between particles.
complex relative permittivity
log frequency
Figure 4.11
The complex relative permittivity and loss tangent of a silty clay soil at a water content of 15% wt (Hoekstra and Delaney [H])
This behaviour is illustrated in Figure 4.11, which shows the complex behaviour of a silty clay soil over the frequency range 103 to 1011 Hz. Although the above is a basic description of a complex subject it does serve to explain the frequency dependent nature of the dielectric properties of the materials involved. This implies that there will be some variation in the velocity of propagation with frequency. Dielectrics exhibiting this phenomenon are termed dispersive. In this situation, the different frequency components within a broadband radar pulse would travel at slightly different speeds, causing the pulse shape to change with time. However, the propagation characteristics of octave band radar signals remain largely unaffected, and most commercial surface-penetrating radar systems fall into this category. The determination of the dielectric properties of earth materials remains largely experimental. Rocks, soils and concrete are complex materials composed of many different minerals in widely varying proportions, and their dielectric parameters may differ greatly even within materials, which are nominally similar. Most earth materials contain moisture, usually with some measure of salinity. Since the relative permittivity of water is of the order of 80, even small amounts of moisture cause a significant increase of the relative permittivity of the material. An indication of the effect of moisture content on the relative permittivity of rock is shown in Figure 4.12. A large number of workers have investigated the relationships between the physical, chemical and mechanical properties of materials and their electrical and in particular microwave properties. In general they have sought to develop suitable
marl
dolomite
er siltstone
siltstone
i sandstone
% water
Figure 4.12
Effect of moisture content of rock on relative permittivity (after Hipp [12])
models to link the properties of the material to its electromagnetic parameters. Such models provide a basis for understanding the behaviour of electromagnetic waves within these media. The influence of moisture content upon the dielectric properties of earth materials is significant and is well documented in the literature. Extensive measurements at 450MHz and 35 GHz were made by Campbell and Ulrichs [13] on dry mineral and rock samples. The difference between the apparent permittivity at the two frequencies was small, supporting their conclusion that dry materials have no measurable dispersion at microwave frequencies. The relative permittivity varied from 2.5 for low-density rock types to 9.5 for high-density basaltic rocks, and the loss tangent (tan S) was -48.5
level at -5OdB
symmetric
2.07
>5
-12
level at - 2 0 dB
symmetric
symmetric
6.3 Amplitude modulation The majority of ground penetrating radar systems have used impulses of radio frequency energy variously described as baseband, video, carrierless, impulse, monocycle or polycycle. The simplified general block diagram of an amplitudemodulated system is shown in Figure 6.14, together with a timing diagram as shown in Figure 6.15. A sequence of pulses, typically of amplitude within the range between 20 V and 200 V and pulse width within the range 200 ps to 50 ns at a pulse repetition interval of between several hundred microseconds and 1 |xs, depending on the system design, is applied to the transmit antenna. It is quite feasible to generate pulses of several hundred kV, albeit at long repetition intervals. The output from the receive antenna is applied to a flash A/D converter or a sequential sampling receiver. This normally consists of an ultra-high-speed sample-and-hold circuit. The control signal to the sample-and-hold circuit which determines the instant of sample time is sequentially incremented each pulse repetition interval. For example, a sampling increment of t = lOOps is added to the previous pulse repetition sampling interval to enable sampling of the received signal at regular intervals, as indicated below: for n — 1 to N
(6.17)
transmitter antenna clock
delay
gen.
8 bit control I/O sampling control 16 bit data output
Figure 6.14
ADC
hold
TVG
receive antenna
sampling head
Transmitter-receiver architecture
clock time
sample pulse
time
RF input signal
time
sampled signal
time
sample and hold O/P
time
ADC window
time
Figure 6.15
Sequential sampling receiver timing
where T is the pulse repetition time, t' is the sampling interval and Af is the total number of samples. Certain important limitations in terms of sampling interval should be noted. From the sampling theorem, the sampling interval must be such as to comply with the Nyquist relationship (6.18) where B is the bandwidth of interest. In practice, a greater number of samples is normally required for accurate reconstruction and the sampling interval is generally taken as (6.19) The principle of the sampling receiver is therefore a down-conversion of the radio frequency signal in the nanosecond time region to an equivalent version in the micro- or millisecond time region. The incrementation of the sampling interval is terminated at a stage when, for example, 256, 512 or 1024 sequential samples have been gathered. The process is then repeated. There are several methods of averaging or 'stacking' the data; either a complete set of samples can be gathered and stored and further sets added to the stored data set or alternatively the sampling interval is held constant for a pre-determined time to accumulate and average a given number of individual samples. The first method needs a digital store but has the advantage that each waveform set suffers little distortion if the radar is moving over the ground. The second method does not need a digital store and a simple lowpass analogue filter can be used. However, depending on the number of samples that have been averaged, the overall waveform set can result in being 'smeared' spatially if the radar is moving at any speed. The stability of the timing increment is very important and generally this should be 10% of the sampling increment; however, practically stability in the order of lOps to 50ps is achieved. The effect of timing instability is to cause a distortion, which is related to the rate of change of the RF waveform. Evidently, where the RF waveform is changing rapidly, jitter in the sampling circuits results in a very noisy reconstructed waveform. Where the rate of change of signal is slow, jitter is less noticeable. Normally, control of the sampling converter is derived from a sample of the output from the pulse generator to ensure that variations in the timing of the latter are compensated automatically. The key elements of this type of radar system are the impulse generator, the timing control circuits, the sampling detector and the peak hold and analogue to digital converter. The impulse generator is generally based on the technique of rapid discharge of the stored energy in a short transmission line. The most common method of achieving this is by means of a transistor operated in avalanche breakdown mode used as the fast switch and a very short length of transmission line. A typical circuit arrangement
input line pulse O/P
to trigger output
Avalanche transistor impulse generator
voltage, V
Figure 6.16
time, s
Figure 6.17
Typical voltage waveform generated by the circuit of Figure 6.16
is shown in Figure 6.16 and this provides an output of 100 V with duration of 1 ns as shown in Figure 6.17. The frequency domain characteristics of such an impulse are shown in Figure 6.18. If shorter duration impulses are required it is possible to use a step recovery diode to generate impulses of durations in the order of 200 ps, and a typical output voltage is in the region of 30 V. Evidently, the repetitive nature of the pulse causes line spectra in the frequency domain. The typical repetition time interval for an avalanche transistor impulse generator is in the order of 0.1 s to 10 s, while the step recovery diode must be chosen specifically to match the repetition interval to ensure that charge carrier recombination can take place.
power, dB m
frequency, GHz
Figure 6.18
Typical spectrum of the waveform generated by the circuit of Figure 6.16
Other methods of generating impulses use power FETs, and voltage impulses up to 1OkV have been generated [10]. An alternative means of generating high power impulses is based on the use of a photoconductive semiconductor switch (PCSS) to discharge a capacitor into a shorted transmission line. A picosecond laser pulse is used to rapidly switch the conducting-nonconducting state of a semiconductive material such as GaAs. Typical output voltages of 14 kV in 50 Q impedance for a duration of nanoseconds or less have been produced [H]. A further variation on this technique is the frozen wave generator shown in Figure 6.19. This consists of several segments of transmission lines connected in series by means of picosecond photoconductive switches. The output from the ensemble is a sequential waveform of arbitrary characteristic, i.e. a 'frozen wave'. Output voltage in the kilovolt range has been generated [12]. Several factors need to be considered in the design of impulse sources, and these are reliability, jitter and repetition rate. In the case of avalanche devices the avalanche process is statistical by nature and is accompanied by jitter. In the case of optical devices the physics of the device must be considered, as the lifetime of the carriers determines the recombination time of the material, and in the case of silicon it may restrict the repetition frequency of the switch. GaAs, on the other hand, exhibits a recombination time of 1 ns. Optical switches may exhibit a reliability of up to 108 operations, which means that their lifetime can be significantly reduced by operation of the radar at high pulse repetition rates. The high speed sampling approach conventionally used to display fast waveforms produces a low S/N ratio because the spectrum of the sampling pulse is a poor match
trigger source
optical splitter
LASS Sl
S2
S3
S4
to load transmission line LASS= light activated silicon switch amplitude
time
Figure 6.19
Frozen wave pulse generator LASS = light activated switch
for that of the received pulse. Being an essentially nonselective filter, it allows large amounts of noise energy to enter the receiver. Also, the sampling circuit tends to add milliamp level unbalanced currents as well as sampling pulse noise to its output. Although a quite acceptable tradeoff for usual laboratory purposes, this may be unacceptable for receivers with sensitivity in the microvolt range.
Alternative methods of data acquisition are based on high-speed analogue to digital converters or the crosscorrelator receiver. There are several methods of acquiring the high bandwidth RF signals output from the receiver: direct analogue to digital conversion using high speed (flash) A-D converters, frequency selection followed by high speed A-D conversion, or sequential sampling. Typical flash A-D converters feature large signal bandwidths of many hundreds of MHz, sampling jitter less than 5 ps and 8-bit resolution. At bandwidths over 500 MHz typical sampling resolutions are 4 bit and a more complex system architecture is found. In general most current generation impulse radars use high-speed A-D conversion receivers for bandwidths below 200 MHz, where greater resolution can be achieved. An alternative receiver architecture is based on subdividing the RF frequency band and mixing the individual band to separate intermediate frequency bandwidths of 200 MHz that can then be separately A-D sampled. The wideband crosscorrelator receiver can use coherent processing and, if required, time dithered decoding. The crosscorrelator is equivalent to a matched filter but has more flexibility. The reference waveform can be matched to the transmitted waveform, or in the case of radar, to the complex signature of a particular target, and can be changed in real time if needed. The components required to construct the crosscorrelator are small, inexpensive, low power and compatible with VLSI techniques. It is thus possible to have a large number of correlators operating independently in parallel to achieve the throughput necessary to provide high resolution, real-time, time-coded operation. Sampling as referred to earlier is a time extending process with which a high frequency repetitive signal is duplicated at a lower repetition rate. This type of sampling, where each sample is taken at a fixed frequency with the period of time between samples remaining constant, is known as coherent sampling. The most basic sampling gate is a simple single diode as shown in Figure 6.20. The diode is essentially a switch, normally 'open' (diode reverse-biased). A short + vbias
Rb.
pulse input
RF input
sampled output
:
Figure 6.20
Single diode sampling gate
CS
+
vbias Rbi
-pulse input Rl
Dl
sampled output
RF input D2
R2
C8
+pulse input
Rb2 "Vbias
Figure 6.21
Dual gate sampling diode
pulse momentarily closes the switch (diode forward-biased), allowing charge to flow from the source to be stored in the capacitor C s , which results in a voltage across C8 proportional to the input signal. The pulse width must be narrow compared to the period of the input signal so that the sample corresponds to a specific portion of the input waveform. The capacitor charging time must be fast enough to accept the charge during this pulse time. The problems of isolation between the signal circuit and the sampling pulse and bias circuits can be serious with the single diode sampler. A two-diode sampler, shown in Figure 6.21, has a low sampling efficiency. The efficiency can be improved by substituting two more diodes for the two resistors in the bridge. The four-diode sampling gate shown in Figure 6.22 is the most commonly used. In a sampling system it would be situated between the input source and the input capacitor of an amplifier. The diodes are normally reverse biased so that the input signal does not cause them to conduct. Sampling is initiated with very narrow pulses, which overcome the reverse bias and switch the diodes into conduction. The low impedance paths allow the amplifier input capacitor to be charged to a voltage proportional to the input voltage. Owing to the short charging time the capacitor may not be charged to the full input voltage. (Some systems include feedback control circuits to continue charging the capacitor in between pulses until the capacitor voltage equals the input voltage.) The capacitor remains charged until the next pulse. The reverse bias applied to the sampling gate diodes is a critical factor in the operation of a sampler. It must be large enough to prevent input signals driving the diodes into conduction and small enough to allow the gating pulses to forward bias the diodes during the sampling periods to achieve maximum sampling efficiency.
+v b i a s
Cc -pulse input D3
Dl RF input
sampled output D4
D2
Cs
C0 +pulse input
-v b i a s Figure 6.22
Quad diode sampling gate
clock
fast ramp CCT
comparator
slow ramp CCT
Figure 6.23
Dual ramp timing circuit
Both dc and ac balance of the sampling gate bridge are essential in achieving the symmetry required for optimum performance of the sampler. The conditions of balance require that the four sampling diodes be matched, the two reverse bias voltages are equal and opposite, and the sampling gate control voltage is identical in wave shape except for polarity. One method of providing identical control gate signals is to derive them from the identical and bifilar-wound windings of a transformer. A narrow pulse can be produced as a result of differentiation of a rectangular pulse with a small coupling capacitor. If required, using step recovery diodes before coupling through the capacitor can reduce pulse rise times. The timing control circuits are a key element of the receiver, and the standard method of generating a sequence of incremented pulses is by means of a dual ramp circuit as shown in Figure 6.23. The fast ramp is at the same rate as the pulse repetition
time = 1 jis a amplitude
time clock waveform b amplitude
time fas* r a m P waveform c amplitude
time slow ramp waveform d amplitude
time inputs to comparator cct. e amplitude
time output from comparator cct.
Figure 6.24
Dual ramp timing waveforms
time, while the slow ramp is set to provide the desired number of samples, i.e. 256, 512 or 1024. The timing sequence for this is shown in Figure 6.24. The ramp circuits can be designed using analogue or digital circuits. In the case of analogue circuits the main building block is an integrator circuit, whereas in the case of a digital design suitable integrated circuits are available in the form of Analog Devices'AD9500 digital delay IC. Evidently, time stability of these circuits is vitally important and, for example, a 512 ns time window with 256 samples requires one sample every 200 ps increment. However, this increment occurs every 1 s, and hence timing stability must be 1 s + 200ps± 20ps, i.e. 1000.2ns ± 20ps, i.e. ±0.002%. Great care is therefore needed in circuit design to achieve adequate stability. The dynamic performance of an impulse (amplitude modulated) radar can be estimated from the following example (see Table 6.2). A graph of received signal strength versus time is shown in Figure 6.25. From this it can be seen that the operating range of the radar system lies between the boundaries defined by the functions defined by the clutter profile, target reflection loss and the limit of sensitivity due to the noise figure of the receiver. It can be readily appreciated that the limited dynamic range of the sampling receiver limits the performance of the radar.
Table 6.2
Typical operating characteristics for a time domain radar
Transmitter Peak power Mean power Antenna and cable losses Peak radiated power Mean radiated power Impulse duration Impulse repetition time System clutter profile (rate of decay of time sidelobes and crosscoupling) Receiver RF bandwidth Equivalent thermal noise (300 k) Noise figure of sampling head Noise floor Maximum input signal level RF dynamic range Time varying gain Equivalent RF dynamic range Averaging signal to noise improvement Receiver equivalent dynamic range
5OW 50 mW — 16.9 dB IW 1 mW 1 ns 1 |JLS 30 dB/ns
(46.9 dBm) (16.98 dB m) (3OdBm) (0 dB m)
1 GHz 4.14 x 10~ 12 W(-84 dB m) 40 dB —44 dB m 7 dB m 53 dB 40 dB 93 dB 25 dB 118 dB
peak receiver input power (+7dB) power, dB m
receiver operating region
clutter level
received signal level
receiver noise (unaveraged) (-44dB)
KTB level (- 84 dB)
time, ns
Figure 6.25
Received signal against time for a sequential sampling receiver
The poor noise figure of the sampling gate can be improved by using a wideband low noise RF amplifier prior to the gate. The typical noise figure of a 1 GHz amplifier is 2.4 dB, and hence an immediate improvement in system noise figure is achieved. However, the sampling gate may now be vulnerable to saturation by high level signals caused by targets at very short ranges. The solution to this problem is to incorporate an additional RF amplifier whose gain can be varied as a function of time. In practice, this is most easily achieved in synchronism with the pulse repetition rate. This avoids undesirable intermodulation effects, which can occur if the gain is changed in real time. This technique enables the receiver to be operated at maximum sensitivity without encountering overload problems. Ideally, the gain/time characteristic should be related to the attenuation and reflection characteristics of the material under investigation. Hence, an adaptive calibration method is advisable. Generally, a compression range of up to 40 dB can be expected, and this is adequate to compress most of the high-level close range signals. The optimum technique is to use an adaptive signal level compression whereby the peak received signal as a function of time is adaptively set to a predetermined value by means of LNA gain adjustment. It is also possible to improve the dynamic range by averaging the received signal, and this improvement is given in dB by (6.20) where TV is the number of averages. However, the rate of improvement quickly decreases as N is increased and, practically, 16 averages provide a reasonable improvement without excessive time penalties. The frequency range of the output signal usually occupies a bandwidth up to 20 kHz. In the case of a radar operating at a repetition rate of 1 |xs with 256 samples, each averaged 16 times, the ensemble down-converted signal is repeated at the time given by (6.21) which, for the values given above, is equal to
Hence the bandwidth of the down-converted signal is given by (6.22) 1
where x is the equivalent down-converted time per sample, and B = \/5xrNa = 12 500Hz. Note that the true noise bandwidth of the receiver is defined by the RF bandwidth, and the noise energy is converted together with the signal. The dynamic range of the analogue to digital converter, which follows the sampling head, should be matched to the dynamic range of the latter and typically, a 12-bit or 16-bit converter is used.
TITLE: 180 mm pipe & water void in sand X scale: 50 File: BR1-15: HP9895, 707.2
Figure 6.26
Example of time-domain signalfrom two buried targets (courtesy ERA Technology) Vertical scale 3 ns = 10 units; horizontal scale 20 mm = 1 increment
When constructing impulse radar systems it is necessary to ensure that adequate decoupling of the internal power supplies is achieved as the effect of impulsive noise from switched mode power supplies on the sampling circuits can result in serious degradation of the overall system performance. Hence, good engineering practice must be maintained in the design and layout of the RF circuits. It is also important to consider the physical layout of the sampling receiver, pulse generator and antennas. Two options are available. The antenna can be directly connected to the transmitter and receiver circuits or it can be interconnected via a length of high quality RF cable. In the latter case the physical length serves to electrically separate the reflected signals caused by the antenna and the transmitter/receiver circuits. However, the cable acts as a lowpass filter, which degrades the system resolution. Where the antennas are directly connected, multiple echoes can prove difficult to reduce to low levels and some design skill is needed to achieve acceptable results. Additionally the physical proximity of electronic components to the antennas may disturb their radiation characteristics. Typical examples of time domain signals received from buried targets are shown in Figures 6.26 and 6.27.
6.4
Frequency modulated continuous wave (FMCW)
Frequency modulated continuous wave (FMCW) radar systems have been used in preference to AM systems where the targets of interest are shallow and frequencies above 1 GHz can be used. As the centre frequency of operation increases it is easier to design and build FMCW radars with wide bandwidths, whereas it becomes progressively more difficult to design AM systems. The block diagram of a typical FMCW radar is shown in Figure 6.28.
time, ns
depth, m
distance, m
depth, m time, ns
distance, m
100 MHz
distance, m
distance, m
depth, m
time, ns
depth, m time, ns
200MHz
5OMHz
Figure 6.27
25MHz
Examples of time domain signals as a function of centre frequency (TNO)
RF subsystem
sweep waveform D/A
VCO error correction
100 MHz clock
discriminator
amplifier 1/r4
control linearising error correction PD
FDt FD
fine range coarse range
Figure 6.28
tracking filter PD = phase detector FD = frequency discrimination FDt = frequency detector output
Block diagram of an FMC W radar system
The main advantages of the FMCW are the wider dynamic range, lower noise figure and higher mean powers that can be radiated. In addition, a much wider class of antennas, i.e. horns, logarithmic etc., is available for use by the designer. In this Section we will consider continuously changing frequency modulation. An FMCW radar system transmits a continuously changing carrier frequency by means of a voltage-controlled oscillator (VCO) over a chosen frequency range on a repetitive basis. The received signal is mixed with a sample of the transmitted waveform and results in a difference frequency which is related to the phase of the received signal - hence its time delay and hence the range of the target. The difference frequency or intermediate frequency (IF) must be derived from an I/Q mixer pair if the information equivalent to a time domain representation is required, as a single ended mixer only provides the modulus of the time domain waveform. In an FMCW radar the transmitter frequency is changed as a function of time in a known manner. If the change is linear then a target return will exist at a time Td given by (6.23) where R is the range in metres and c is the velocity of light in metres per second. If this target return signal is mixed with the transmitted signal, a beat frequency, termed the IF (intermediate frequency), will be produced. This will be a measure of the target range, as shown in Figure 6.29. If the transmitted signal is modulated with a triangular modulating function at a rate over a range,
a
target returns transmitter frequency time RF transmitter and received waveforms
b difference frequency time receiver output
c power spectral density
difference frequency or range line separation frequency spectra of receiver output
Figure 6.29
FMC W tim ing diagram and IF waveforms
then the intermediate frequency is given by (6.24) where fm is the modulation frequency in Hz and A / is the frequency deviation in Hz. The choice of modulating waveform defines the resultant IF spectrum, and it is desirable to minimise the bandwidth of the IF spectrum due to a single target in order to optimise the target resolution. If the IF were generated by a continuous linear frequency deviation, then the IF spectrum would consist of a sum and difference frequency, a dc component and various other frequencies resulting from the mixer's nonlinear properties, assuming that the mixer had a perfect square law characteristic. For practical purposes, only the difference frequency will be considered. However, the repetitive nature of the modulating waveform causes points in the IF time waveform where the amplitude drops to zero. This can be regarded as an amplitude modulation of the IF signal. If the case of a single target is considered, then the IF waveform as a function of time would be given by (6.25) The repetitive nature of the RF sweep effectively convolves the basic IF waveform with line spectra (6.26) The Fourier transform of (6.27) (6.28) The Fourier transform of f'm (t) can be derived after rearranging the integration period:
Rearranging the time axes:
(6.29) where n is the harmonic number, (6.30)
where T' — (T — r), and (6.31) Hence the IF spectrum is given by
(6.32) It can be seen that the periodic IF signal consists of an envelope function, (sin JC)/JC, enclosing a line function. In essence, the FMCW radar measures the phase of the IF signal, which is directly related to the target range. The frequency of the IF signal can be regarded as a measure of range. An inverse frequency-time transform can reproduce a time domain equivalent to the impulse radar. The FMCW radar system is particularly sensitive to certain parameters. In particular, it requires a high degree of linearity of frequency sweep with time to avoid spectral widening of the IF and hence degradation of system resolution. This effect can be illustrated by considering the case of FMCW radar with varying degrees of nonlinearity as shown in Figures 6.30 and 6.31. The IF spectrum is shown
power, dB
FFT, IF power spectrum (dB), 0% sweep nonlin, 0 dB ripple
frequency, Hz
Figure 6.30
IF power spectrum for zero sweep nonlinearity (courtesy ERA Technology)
power, dB
FFT, IF power spectrum (dB), 0.5% sweep nonlin, OdB ripple
frequency, Hz
Figure 6.31
IF power spectrum for 0.5% sweep nonlinearity (courtesy ERA Technology)
for two cases: (a) perfect (zero nonlinearity) and (b) 0.5% nonlinearity. The main effect is to broaden the width of the IF spectrum as the extent of nonlinearity increases and increase the sidelobe level. Practically a useful system should aim to keep all nonlinearities Sxx. As Sxy and Syx tend to zero, then the backscattered E field is largely parallel to the target axis in the case of a parallel incident E field applied to a linear metallic target. When a plastic pipe is illuminated with an orthogonal incident E field the backscattered E field is the largest component of the reflected signal.
Figure 6.51
Holographic data from two orthogonal scans: (a) data; (b) subtracted; (c) focused in the object plane (after Junkin)
Many systems have exploited this polarisation sensitivity by using orthogonal transmit and receive antennas. The crossed dipole exhibits a much lower crosscoupling than a copolarised pair and this improves the system detectivity. It is well known that targets such as pipes, as well as shells of various calibres and cracks, act as depolarising features. A linearly polarised crossed dipole antenna rotated about an axis normal to the target produces a sinusoidal variation in received signal. However, the null points are a distinct disadvantage because the operator is required to make two separate, axially rotated measurements at every point to be sure of detecting pipes at unknown orientations. If such a crossed dipole is rotated around its own axis, the amplitude of the received signal will vary sinusoidally with the angular rotation of the antenna. Following Daniels et al. [41], (6.59) Hence if Sxy and Syx are neglected, then (6.60) In real life, additional received signals caused by a variety of factors such as changes in crosscoupling between the crossed dipoles due to objects or variations in local impedance on the ground surface will contribute to Er, which can be rewritten as Er = KicosO + K2Et{(Sxx
- Syy)sm20}
(6.61)
The need for rotation of the antenna is physically restrictive, and electronic means of rotation have been considered. One design possibility is to synthesise a circularly polarised signal. Any wave of arbitrary polarisation can be synthesised from two waves orthogonally polarised to each other. As shown in Chapter 5, Section 5.8, a circularly polarised wave is produced by exciting vertically and horizontally polarised waves, each having the same amplitude and with a 90° phase difference between them. The radiating elements are fed, via wideband (preferably decade) 180° and 90° hybrids, to radiate circular polarisation. If right-hand circularly polarised signals are transmitted and received, the preferential detection of linear features is achieved. If, however, right-hand circularly polarised signals are transmitted and left-hand circularly polarised signals are received, planar features are detected. Hence, if connections to the radiating elements are arranged and switched appropriately, the signals routed to the receiver contain different data according to the sense of polarisation. The data, therefore, can be processed separately and in a different manner to provide images of different targets in the material under investigation. Unfortunately hardware deficiencies limit the performance; firstly, it is difficult to achieve wideband operation with 90° hybrids (at least over a decade) and, second, even the fastest state-of-the-art GaAs switches have unacceptably high break-through levels.
In view of these difficulties the feasibility of using a commutated multi-element crossed dipole array can be considered, and this technique is rotating linear rather than circular polarisation. A simple option is an eight-element antenna in which the crossed dipole pairs can be switched at intervals of up to 1 ms so that the two crossed dipole pairs are orientated between 0° and 45° as shown in Figure 5.47. This antenna proved to be successful proof of the concept demonstrator. Full commutation over 360° in 45° steps could be achieved as shown in Chapter 5, Section 5.8 by using PIN diode switches (to handle the transmitted power) operating at a switching interval of 1 s, thus achieving 360° rotation in ~10 s. The possibility of real time discrimination using filters based on recognition of the cos 20 amplitude variation of each range sample is also possible. Operationally, such a system would have the advantage of being able to survey rapidly without the limitations imposed by mechanically rotated antennas. Conventionally, circular polarisation refers to a steady-state condition during which a long duration pulse or CW waveforms are transmitted. For impulse radars, the pulse duration is very short ( 1. The regularisation parameter can be chosen via comparison between the discrepancy and the assumed bound for the noise level. The direct application of the Morozov criterion to Tikhonov regularisation requires the computation of a solution to (7.90), the subsequent reconstruction and the check whether the condition (7.92) is satisfied. If not, it is necessary to change a and to repeat the procedure until (7.92) holds. One can use another implementation of the discrepancy principle (7.93) for some /3 satisfying a < fi < 2a. The steps to process the explicit algorithms of the deconvolution can be written as follows. 7.7.3.1 Algorithm 1. Direct Tikhonov regularisation with the discrepancy principle: 1. a o = 5 i , T = 1.1. 2. For k = 1,2, ...,A/" (loop with the increasing a), evaluate \k(^k-\) and X£(2G?£-I) according to (7.90). If (7.93) is satisfied then halt processing and the final solution x^ = x^ (ctk-1). If (7.93) is not satisfied then ak = 2ak-\ and continue the loop.
3. 4.
If the solution has not been determined, then evaluate the same loop for decreasing a with a/c = a/c-i/2. The number of steps Af must be limited by appropriate maximal time for solving the task.
This algorithm is a straightforward implementation of Tikhonov regularisation and is not efficient from a computational point of view. Another a posteriori approach to find out a deals with a nonlinear matrix equation [69, p. 123] (7.94) Having solved that equation, we can obtain a best-approximate solution with only one computation of (7.90). The main computational burden here is referred to solving (7.94), which is a difficult task and requires the implementation of a separate iterative algorithm. 7.7.3.2 Algorithm 2. Direct Tikhonov regularisation with the nonlinear equation: 1. ao = si,T = l.l. 2. Evaluate (7.94) to find out an optimal a. 3. Evaluate (7.90) to find out a regularised solution x^. The described direct methods and algorithms always have a solution even in the case of underestimated noise level. Iterative regularisation methods. Unlike the direct methods of regularisation, the iterative methods do not include sophisticated computations and therefore they are considerably faster for big vectors and matrices. Also those methods do not require large computer resources. In the meantime, the iterative methods provide good accuracy. Their drawback is sensitivity to the noise level. If this is underestimated, then the methods do not converge and so do not have a solution at all. Most iterative methods are based on a transformation of the normal equation into equivalent equations like (7.95) A classical iterative method illustrating this transformation is the Landweber iteration (7.96) The iteration index k plays the role of the regularisation parameter a and the stopping rule plays the role of parameter choice method. For the Landweber iteration the Morozov criterion is usually applied as a stopping rule.
One of the accelerated iterative methods is a v-method of regularisation [69, p. 167], (7.97) The use of difference between results of two preceding iterations improves the speed of convergence. The parameter v represents the order with which the approximation error decreases: (7.98) Also v controls an asymptotic growth of coefficients /x^ and cok, and consequently the speed of convergence. The parameter v can be chosen equal to 1. Numerically it is more efficient to base the computation of x^ on intermediate quantities z8k via x^ = HTz£. With respect to that, the following algorithm of deconvolution has been developed. 7.7.3.3 Algorithm 3. Iterative regularisation with v-method 1. 2. 3.
I f ^ < r5 2 , then stop. 4. The final solution x8 =
(7.99)
Note that the convolution matrix should be normalised before its first use in the algorithm and at the final step the matrix should be restored after satisfying the stopping rule at the £th iteration; z|—1 is required for the final solution. 7.7.3.4 Data noise level estimation: accuracy and stability of deconvolution: The art of applying the regularisation methods to deconvolution is to find out the right compromise between accuracy and stability of the approximated solution. Accuracy is characterised by the norm of the difference between the given and reconstructed data I y8 — Hx8a I, stability by norm of the approximation || x£ ||. Deconvolution stability or, more accurately, its instability, appears as ringing in the deconvolved vector x^. The plot of log Ix^, I versus log \\y8 — Hx* || gives an L-curve, which is used in heuristic methods. If the residual norm is small (case of high accuracy), then ||x* || changes drastically in dependence on a and represents the vertical part of the L-curve. If I y8 — Hx* I is big enough, then ||x* || becomes stable and represents the horizontal part of the L-curve. In a posteriori regularisation methods both accuracy and stability depend on the noise level of the data. The task is to find out that level. Consider the energy of a noisy vector: for an additive white noise the total vector energy equals the sum of the signal and noise energies: (7.100) So the noise level can be defined as the norm of the noise vector: (7.101) Also we can confirm this definition with the discrepancy principle. In the ideal case, when the reconstructed data coincide with the exact data, (7.92) can be rewritten as (7.102)
Obviously, the noise level can be found with the statistical approach (7.103) where the operator E{o} stands for averaging, o is noise standard deviation and N is the length of the vector. Equation (7.103) determines the maximal noise level, which provides excellent stability of the deconvolution results. However, numerical experiments with the real GPR data showed that accuracy of the regularised deconvolution can be significantly improved without loss of stability for a noise level lower than (7.103). It can be explained that accuracy depends on the signal to noise ratio (SNR) rather than on the noise content in a received signal. We propose another approach to estimate the noise level. Consider the energy of noisy data,
which we rewrite as
The maximal or peak SNR
Now we can obtain an estimate of noise level as
(7.104) So we receive the lower estimate of noise level, which maintains stability and results in better accuracy than (7.103). Equation (7.104) is an adaptive algorithm with respect to the received signal. Unlike (7.103) it estimates for a certain signal its own noise level relatively to the maximal signal's peak. The noise deviation of the measuring system noise can usually be estimated before experiments and used as a parameter for deconvolution algorithms. The estimation of noise level based on peak SNR fits well in the processing of nonstationary rapidly decaying signals as UWB signals are. For the accuracy estimation, we propose to use the normalised RMS error (7.105) This can be interpreted as the relative distance between two vectors to be compared. It is 0 when the vectors coincide and 100 per cent when the vectors have the same origin, length and opposite directions. 7.7.3.5 Numerical results: The first trial to check how regularised deconvolution works, is deconvolving data out of the same data. Theoretically, it must result in a delta-function. We make this auto-deconvolution using the v-method and Algorithm 3 for the impulse response depicted in Figure 7.44. The estimate of noise standard deviation is a = 1.7613 x 10~4. The noise level is defined according to (7.104). The result of the deconvolution shown in Figure 7.45 is not a delta-function. Obviously, the more accurate the deconvolution the closer its result to a delta-function. The relative distance between the original and reconstructed impulse response is 0.21%. For noise level defined from (7.103) this distance is 0.89%. Now we divide a by 1000
result of autodeconvolution
time, ns
Figure 7.45 Autodeconvolution with noise standard deviation estimate a 1.7613 x 10~4
=
and substitute it into (7.104). Its result represented in Figure 7.46 is a delta-function. The corresponding relative distance equals 0.0002%. Auto-deconvolution remains stable independently of the estimate of noise level because the convolution matrix is formed from the input data. Auto-deconvolution illustrates the possibility to decrease intentionally a parameter standing for noise level in order to obtain better accuracy. Now consider deconvolution for a signal from an anti-personnel mine PMN-2. The signal was received by a GPR with impulse response and noise deviation mentioned above. Deconvolution has been carried out using Algorithm 3. The fixed noise level estimate (7.103) resulted in error of deconvolution of 13.78% (Figure 1.47b), while the estimate (7.108) resulted in an error of 1.60% (Figure 1 AIc). The use of noise standard deviation a/10 in (7.108) resulted in an error of 0.21 % but with considerable ringing (Figure 7.48J). These results show that the use of the adaptive noise level estimate (7.108) provides excellent accuracy of deconvolution with minimal ringing. As shown in Figure 7.48, deconvolution shifts the signal back in time by effective duration of the GPR impulse response, depicted in Figure 7.44. In that particular example, the shift is about 1 ns, corresponding to the duration of the most energetic part of the impulse response. This is the fundamental effect of deconvolution which should be accounted for GPR signal processing. Since the GPR impulse response remains the same, the time shift is constant.
result of autodeconvolution
time, ns
Figure 7.46
c
reconstructed signal with accuracy 1.60%
reconstructed signal with accuracy 13.78% d
reconstructed signal with accuracy 0.21%
time, ns
time, ns
original signal
a
b
Autodeconvolution with intentionally decreased noise standard deviation estimate a/1000 = 1.7613 x 10~7
Figure 7.47
Original (a) and reconstructed signals: (b) fixed noise level estimate; (c) adaptive noise level estimate; (d) adaptive noise level estimate with a/10
a
original signal
c
b
deconvolved signal with accuracy 13.78%
d
time, ns
deconvolved signal with accuracy 1.60%
deconvolved signal with accuracy 0.21%
time, ns
Figure 7.48 Original (a) and deconvolved signals: (b) fixed noise level estimate; (c) adaptive noise level estimate; (d) adaptive noise level estimate with o/10
7.7.3.6 Comparative performance of the deconvolution algorithms: For comparison of performances, the deconvolution algorithms 1-3 have been implemented for the signal depicted in Figure 7.47. The length of corresponding vectors was 512 elements, and the size of the convolution matrix was 512 by 512. The adaptive noise level estimate was used. The comparison was based on three factors: accuracy (the relative distance); computational speed (time of computation and number of iterations); computational burden measured by a number of floating point operations (FLOPS). The time of computation and the number of FLOPS which are required for executing a program can be obtained with built-in MATLAB routines. Performance of the deconvolution algorithms is represented in Table 7.1. The first two algorithms are direct with respect to a solution, but iterative with respect to the regularisation parameter, which is why their computational speed is measured in iterations. The time of computation depends on computer performance and can be considered only as a comparative index, while other figures remain the same on different computers. The iterative algorithm with the v-method showed the best performance. It is the fastest, most accurate and most economical algorithm in comparison with other algorithms.
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Table 7.1
Relative performance of deconvolution algorithms
Algorithm
Error, % Computational speed
Computational burden
l.Tikhonov with the discrepancy principle 2. Tikhonov with the nonlinear equation 3. v-method
1.84
10506 MFLOPS
5.07 1.60
159.23 s 6 iterations 1118s 29 iterations 7.42 s 10 iterations
98411 MFLOPS 373 MFLOPS
7.7.3.7 Summary: Deconvolution in UWB signal processing is an ill posed inverse problem. Tikhonov regularisation and the v-method were considered for its solution. The data noise level should be defined as a compromise between accuracy and stability of deconvolution, and an adaptive noise level estimate has been proposed. The relative distance between an original signal and its reconstruction has been proposed as a numerical measure of deconvolution accuracy. Two direct and one iterative deconvolution algorithm with regularisation were developed and tested, and the iterative algorithm with v-method showed the best performance.
7.8
Multi-fold, multi-component and multi-azimuth GPR for sub-surface imaging and material characterisation Prof. Michele Pipan, Emanuele Forte, Giancarlo Dal Mom, Monica Sugan and Icilio Finetti
7.8.1
Introduction
GPR can provide shallow sub-surface images sharper than any other geophysical technique in the 0-5 m depth range and quantitative information about EM properties of materials. It is therefore best suited for the noninvasive high-resolution study of the near surface. Advances in UWB equipment and dedicated data processing methods have recently improved performances of GPR and fostered the successful application of the method at depths ranging from a few centimetres (UXO detection) to different kilometres (glaciology), as illustrated by several examples in this book. The two crucial tasks of the noninvasive method, namely sub-surface imaging and characterisation of materials, are best accomplished by GPR methods that exploit redundant information. In this Section we show examples of successful application of such techniques, in particular linear multi-fold, azimuthal multi-fold and multipolarisation (multi-component) methods. Focusing of the radar wave field and clutter reduction are the key issues in image enhancement. Focusing is based on migration techniques that require knowledge of the velocity of radar waves in the sub-surface. Clutter reduction benefits from multiple
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Table 7.1
Relative performance of deconvolution algorithms
Algorithm
Error, % Computational speed
Computational burden
l.Tikhonov with the discrepancy principle 2. Tikhonov with the nonlinear equation 3. v-method
1.84
10506 MFLOPS
5.07 1.60
159.23 s 6 iterations 1118s 29 iterations 7.42 s 10 iterations
98411 MFLOPS 373 MFLOPS
7.7.3.7 Summary: Deconvolution in UWB signal processing is an ill posed inverse problem. Tikhonov regularisation and the v-method were considered for its solution. The data noise level should be defined as a compromise between accuracy and stability of deconvolution, and an adaptive noise level estimate has been proposed. The relative distance between an original signal and its reconstruction has been proposed as a numerical measure of deconvolution accuracy. Two direct and one iterative deconvolution algorithm with regularisation were developed and tested, and the iterative algorithm with v-method showed the best performance.
7.8
Multi-fold, multi-component and multi-azimuth GPR for sub-surface imaging and material characterisation Prof. Michele Pipan, Emanuele Forte, Giancarlo Dal Mom, Monica Sugan and Icilio Finetti
7.8.1
Introduction
GPR can provide shallow sub-surface images sharper than any other geophysical technique in the 0-5 m depth range and quantitative information about EM properties of materials. It is therefore best suited for the noninvasive high-resolution study of the near surface. Advances in UWB equipment and dedicated data processing methods have recently improved performances of GPR and fostered the successful application of the method at depths ranging from a few centimetres (UXO detection) to different kilometres (glaciology), as illustrated by several examples in this book. The two crucial tasks of the noninvasive method, namely sub-surface imaging and characterisation of materials, are best accomplished by GPR methods that exploit redundant information. In this Section we show examples of successful application of such techniques, in particular linear multi-fold, azimuthal multi-fold and multipolarisation (multi-component) methods. Focusing of the radar wave field and clutter reduction are the key issues in image enhancement. Focusing is based on migration techniques that require knowledge of the velocity of radar waves in the sub-surface. Clutter reduction benefits from multiple
data from the same sub-surface location. Multi-fold methods can provide an adequate solution for both problems. Target characterisation implies reconstruction of images where properties of subsurface scatterers are correctly represented. Multi-component imaging algorithms can accomplish such tasks [70], which exploit knowledge of transmitter and receiver antenna radiation characteristics and incorporate wave speed, polarisation and amplitude of the scattered electric field. However, the data acquisition and computational costs of such methods do not presently allow their extensive application but for academic purposes. An alternative strategy is based on the analysis of amplitude variations versus azimuth and offset at different polarisations. The cost of such approaches is limited and the technique allows us to optimise data acquisition parameters in single-fold and multi-fold surveys depending on target characteristics.
7.8.2 Data acquisition We used a Mala Geoscience RAMAC system, equipped with 250, 500 and 800 MHz shielded antennas, to obtain all the radar datasets shown in this Section. Multiple common offset data acquisition schemes, i.e. iterated data acquisition along the same profile using different transmitter-receiver antenna separation, are a convenient solution to obtain multi-fold datasets in case a multi-channel system is not available. In the latter case, however, the difficulty of sliding multiple antennas at constant offset on rough surfaces may seriously hamper multi-fold data acquisition. Frames and numerically controlled systems are used for accurate and cost effective multi-offset/multi-component data acquisition in the case of laboratory experiments or measurements performed over small areas. Such solutions are further implemented in commercial systems, mainly for underground utilities detection. In the present study, we have used shielded antennas kept at fixed distance and orientation by Kevlar strings.
7.8.3
Data processing
The basic processing sequence for single-fold and multi-fold data (when treated as separate common-offset) is reported in Table 7.2. Sequence 1 produces the filtered section where the position of the imaged targets is not correct and diffraction hyperbolas are not collapsed. Such a section can be exploited to reconstruct sub-surface models in the case of azimuthal isotropy, i.e. for horizontally layered media and vertical velocity variations only. Identification of point and linear scatterers such as, for example, underground utilities perpendicular to the GPR profile, can be further successfully performed, provided that diffraction hyperbolas do not smear the response and decrease resolution below the threshold requested for the interpretation of the targets. Sequence 2 produces the migrated and filtered section, which should provide a better sub-surface reconstruction. It should be stressed that the order of migration and filtering cannot be interchanged, unless the transfer function of the filter is kept constant in time, which means that the filter is not time-variant. This can be done in particular when shallow conductive layers (such
Table 7.2 Basic processing sequence for single-fold and multi-fold data (as separate common offset) Dewow Background removal Amplitude correction Deconvolution 2 Migration Time-variant filtering (TVF)
Table 7.3
Processing sequencesfor multi-fold data, vertically varying velocity field
a Dewow b Background removal c Preliminary amplitude correction d Pre-stack gather editing e Deconvolution f Velocity analysis g Velocity based amplitude correction h Pre-stack coherent noise removal Stack 4 Post-stack depth migration (DM) Depth-variant filtering (DVF)
as clayey soils) or large numbers of scatterers reduce the penetration. The number of samples available in the useful part of the GPR section is then too small to allow the application of a time-varying operator. We apply different processing sequences to multi-fold data depending on the velocity field characteristics. The basic sequences are reported in Tables 7.3 and 7.4. This choice is not only related to structural characteristics of the sub-surface volume, as in the case of horizontally layered soils that exhibit horizontal velocity gradients due to variations in water content. In such cases, time migration techniques are inadequate. Mild and severe horizontal velocity variations require application of sequences 5 and 6, respectively. Crucial steps in the imaging process are pre-stack coherent noise removal (see, for example, References [71, 72]) and those involving the analysis and reconstruction of the velocity field, namely step i in sequence 5 and j , k, 1 in sequence 6. DMO processing (i) implies a two-step velocity analysis, before and after application of the DMO correction (see, for example, Reference [73]).
Table 7.4 Processing sequences for multi-fold data, vertically and laterally varying velocity field Steps a to h from Table 7.3 6 j Initial velocity-depth model building k Kirchhoff pre-stack depth migration (PSDM) 1 Velocity-depth model upgrading Final Kirchhoff PSDM DVF
In the case of severe lateral radar velocity variations, our strategy encompasses an initial velocity-depth (V-z) model building (j) in two steps: we first convert root mean square velocities (VRMS) obtained from CMP analysis into interval velocities (VINT) as a function of time by applying a horizontal smoothing. We then convert VINT(O to VINT(Z) by applying a vertical smoothing. The two-step smoothing proves effective in processing data from shallow sediments, where variable water content and prograding or accretionary structures introduce rapid velocity variations. V-z models are updated after PSDM by means of residual moveout analysis performed on common reflection point (CRP) gathers. Two main benefits can be expected from accurate V-z model reconstructions, namely improved sub-surface images and information about variations in the dielectric constant, which for low-loss (i.e. tan 8 < 1) materials is directly related to the radar wave velocity. Such information cannot be attained by single-fold methods.
7.8.4 Results Figure 7.49 shows an example of common mid point (CMP) gather obtained in sediments of an alluvial plain in northern Italy. The low attenuation and homogeneous characteristics of each sedimentary layer (from sands to gravelly sands) are responsible for the wide offset range (0.5-4.2 m) and excellent response in the far offset range (Figure 7.49a). The ground wave (G) allows a straightforward determination of near surface velocity, while reflections (R) are clearly interpretable in the full twoway-time range (up to 180 ns). The normalised crosscorrelation velocity spectrum (Figure 7A9b) exhibits well focused coherency values due to the high signal-to-noise ratio (SNR > 30 dB), even if departures from hyperbolic moveout arise from minor lateral velocity variations and prevent a perfect moveout correction (Figure 7.49c). A comparison between different imaging strategies is shown in Figure 7.50. The GPR profile crosses a prograding structure related to the progressive accumulation of sediments deposited by a stream over a series of flat layers. Figure 7.50b shows the image enhancement provided by a 1200% stack in comparison with the single-fold section of Figure 7.50a. The complete series of foresets is clearly interpretable in the stack section as well as the flat underlying sedimentary sequence. A strong basal reflector shows up at ~ 100 ns in the single-fold and stack record,
Figure 7.49
b
velocity, cm/ns
offset, m
(a) Example of 250 MHz large offset-range CMP (0.5-4.2 m) from an alluvial plain in northern Italy after processing: (A) Air wave, (G) ground wave, (R) reflections; (b) normalised cross correlation velocity analysis with superimposed velocity function; (c) CMP after NMO correction
a
b
distance, m
trace no. distance, m
C
C
time, ns
offset, m
time, ns
time, ns
a
d trace no.
distance, m
Figure 7.50
(a) 250MHz single-fold section (offset 1.2 m) from the Isonzo river bank (Italy) after standard processing; (b) stack section (1200% fold); (c) post-stack Kirchhojf time-migrated section; (d) pre-stack Kirchhoff depth-migrated section: (B) base of agricultural layer, (P) prograding alluvial sequence, (H) top of flat layer, (W) water table
which is related to the water table. The correct structure of the prograding sequence and the erosional channel located between 0.0 and 2.5 m are properly imaged in the migrated sections of Figure 7.50c, d. PSDM is not always necessary to produce a correct image from multi-fold data, as demonstrated by the example of Figure 7.51. Stack 500MHz data (Figure 7.5 Ib) from a sandy beach in north Italy allow the identification of gently dipping layers that cannot be interpreted in the single-fold section of Figure 7.51a. Post-stack F-K migration (Figure 7.51c) reconstructs the correct dip of layer boundaries (L) and location of the discontinuity (D) by focusing the diffraction hyperbolas where the layer boundaries show an interruption, possibly due to differential compaction or human activity (excavation). The benefits of 2D multi-fold imaging can be extended to the reconstruction of 3D sub-surface models by combining multiple sections (Figure 7.52). This is of particular interest to avoid mis-ties, to correlate fractures and faults and to reconstruct complex sub-surface structures, as in the case of archaeological targets. The example in Figure 7.52 successfully images a soil-limestone contact and allows a detailed reconstruction of bedrock topography and related structures. An alternative strategy is to cut the data volume along planes or irregular surfaces. Horizontal cuts are known as time-slices and are extensively used in archaeological and engineering applications. The example in Figure 7.53 shows the reconstruction of a buried rain-water tank in vertical (A) and horizontal (B) cross-section. Steel rebars spaced 4 m apart are successfully imaged both by the vertical and horizontal cross-sections. In the case of deeper targets and less favourable SNR, the identification of weak reflectors in noisy background may require the application of further data processing procedures, such as computation of instantaneous attributes and dedicated coherent noise removal techniques. The pre-stack domain allows the application to a variety of records, such as common offset sections, common shot or common mid point gathers. Separate processing of such records results in enhanced stack and migrated data. The example in Figure 7.54 shows that the stack of instantaneous phase common offset sections computed by means of wavelet transform [74] allows enhanced interpretation of echoes from a series of dipping reflectors (D) beneath waste (C). Controlled conditions allow an analysis of the performances of multi-fold/multiazimuth techniques. In Figure 7.55, we show the comparison of synthetic and real 800MHz data obtained from a sandbox facility with buried pipes of different characteristics (metal/PVC; PVC filled by different fluids; 10 cm diameter, 40 cm depth). The correspondence between numerical simulation and field data is apparent. If we extend the analysis to different offsets and azimuth we obtain a double result. We can identify the content of the pipe based on the different response as a function of azimuth and offset (Figure 7.56, rows A and B). In this case, a reflector beneath the pipe allows a more reliable discrimination that is less affected by the quantity of fluid within the pipe (Figure 7.56, row A). We can further exploit the amplitude versus offset/azimuth (AVOA) analysis to identify the optimum offset/azimuth combination, which provides the highest amplitude response in the perspective of extensive surveys for buried utilities detection. A preliminary
time, ns
a trace no. distance, m
time, ns
b trace no. distance, m
time, ns
c trace no. distance, m
Figure 7.51
(a) 500MHz single-fold section (offset 0.6 m) from a sand beach (Italy) after standard processing; (b) stack section (1000% fold); (c) post-stack F-K migrated section: (L) moderately dipping layers with different slopes, (D) example of lateral discontinuity
trace no.
trace no.
Figure 7.52 Example of 3D visualisation of a 500MHz GPR stack dataset (1200% fold)
AVOA test performed in the area of interest allows an optimised selection of data acquisition parameters. Target characterisation and selection of optimum data acquisition parameters can be extended to the case of multiple polarisations, as illustrated by Figure 7.57 (800MHz data). Columns 1 and 2 refer to co-pole and crosspole configuration, respectively, while rows A and B report the results from PVC pipe (10 cm diameter, 40 cm depth) filled by air and freshwater, and row C is the response of a metal pipe. In the case of cylindrical targets, such as pipes, the response is in good agreement with well established theoretical models. In the case of more complex targets, such as buried cultural heritage, vertical or lateral coherence (i.e. target geometry) is not always adequate to discriminate potential targets, and the AVOA response for different antenna configurations (co-pole, crosspole) can be exploited to classify the echoes and perform a target-oriented interpretation.
a A
concrete walls
B
rebars
time, ns
time, ns
trace no. distance, m
b B
Figure 7.53
(a) 400MHz stack section of a concrete platform with rebars; (b) 11 ns timeslice (about 40 cm) across the stack GPR data volume
time, ns
depth, m
a
time, ns
depth, m
b
c
W
Figure 7.54
D
depth, m
time, ns
C
(a) 250MHz single-fold section (offset LOm) from a brownfield; (b) stack section (1200% fold); (c) instantaneous phase of stack section: (W) base of waste disposal, (C) chaotic zone, (D) dipping horizons
A
1 model 1
2 model of air filled pipe
3 real data of air filled pipe
B
model 2
model of metallic pipe
real data of metallic pipe
C
model 3
model of water filled pipe
real data of water filled pipe
Figure 7.55 Columns 1 to 3: (1) sub-surface model usedfor numerical simulation, (2) synthetic GPR data (FDTD numerical simulation) and (3) real GPR data. Rows A to C: (A) air filled PVC pipe, (B) metallic and (C) fresh water filled PVC pipe The pipe was placed into a sandbox with metallic bottom
7.8.5 Discussion Multi-fold methods offer data redundancy that can be successfully exploited to obtain enhanced sub-surface images, discriminate coherent noise from signal, and evaluate EM properties of soils, rocks and buried targets. Pre-stack depth migration techniques allow imaging in complex sub-surface conditions and reconstruction of accurate V-z models, which are of interest for the analysis of vertical and lateral variations of the dielectric constant. Data derived spatial stacking operators (see, for example, Reference [75]) are an alternative imaging solution that does not depend on the V-z model but are based on data-derived kinematic attributes. Such attributes can be determined by means of optimisation procedures and successively exploited to
azimuth, deg.
azimuth, deg.
azimuth, cleg.
4 bottom salt 35
3 bottom gasoline
offset, cm
offset, cm
top air
top water
top gasoline
top salt 35
offset, cm
Figure 7.56
azimuth, deg.
azimuth, deg.
offset, cm
azimuth, deg.
offset, cm
azimuth, deg.
B
2 bottom water
bottom air
azimuth, deg.
1 A
offset, cm
offset, cm
offset, cm
GPR AVO (amplitude versus offset) and AVA (amplitude versus azimuth) analysis performed on a PVC pipe filled with different fluids Columns 1 to 4: (1) air, (2) fresh water, (3) gasoline and (4) salt water (salinity about 35%). Rows A and B: (A) amplitude of reflection from metal base and (B) amplitude of reflection from top of the pipe
obtain the V-z model. This is certainly a promising strategy, particularly in complex sub-surface conditions where the interpretation of pre-stack and common-offset data is difficult and an interpretive approach to V-z model reconstruction is not feasible. AVOA analysis offers a solution to characterise and classify sub-surface targets, which may be effectively implemented by exploiting multi-channel systems. The data redundancy provided by the multi-fold method not only enhances processing and imaging results but also improves the interpretation of complex targets, as in the case of archaeological applications. The combined interpretation of pre-stack data (CMP and CRP gathers, common-offset sections at different offsets) and stack or migrated data allows discrimination of coherent noise from signal, the identification of weak signals in noisy background and the tracking of complex and irregular reflectors buried in chaotic soils. Such tasks exploit primary signal coherency in the
A
B
2
D
1
E
C
Figure 7.57
Multi-azimuth analysis of the GPR responsefrom pipes (800 MHz GPR data from sandbox). Columns 1 and 2: (1) Co-pole and (2) crosspole configuration. (A)-(D) air filled PVC pipe, (B)-(E) fresh water filled PVCpipe and (C)-(F) metallic pipe
pre-stack domain and analysis and comparison of target response in the near and far offset range. The elusive nature of archaeological targets, whose dimensions, shape, orientation and physical properties are most often unknown and which are in many cases characterised by low contrast (such as mud-bricks in loams), requires a multi-fold approach to obtain the necessary constraints for a reliable sub-surface model.
7.9
Microwave tomography Prof. Rocco Pierri, Angelo Liseno (Seconda Universitd diNapoli) and Raffaele Solimene (Universitd Mediterranea di Reggio Calabria)
7.9.1
Introduction
Ground penetrating radar generally produces an image which requires considerable skill, ability and experience in interpretation of data to detect and localise multiple targets, and this unavoidably introduces an element of subjectivity to the process. The scientific community has endeavoured, during recent years, to develop techniques in order to make the analysis more 'objective'. The technique under consideration is the tomographic approach [76], which consists in determining an image of the spatial features of the object. This allows detection and localisation of the object as well as the ability to retrieve information about its shape, dielectric permittivity and conductivity. Tomographic techniques are fraught with the difficulty of processing the data to find a solution of the mathematical relationship between the quantities to plot (i.e. the dielectric permittivity and conductivity profiles) and the measurements of the scattered field [77]. This Section considers the problem that we will henceforth illustrate - that of reconstructing the electromagnetic properties of an object (permittivity and conductivity) from measurements of certain 'observable' quantities (the electromagnetic scattered field), which is also known as an electromagnetic scattering inverse problem [78]. Conceptually, this is not much different from other possible inverse problems arising, for instance, from the use of acoustic waves [78]. The only difference lies in the involved equations and in that, while our purpose is to 'see' the interior of an object through microwaves, in acoustics one aims at 'hearing' the characteristics of the scatterer under test [79]. Before proceeding further, it is necessary to note that the possibility of 'looking' at the interior of an object is based on the fact that the incident wave penetrates inside the object itself, collects information about its interior and finally is scattered, delivering such information to the sensors. Although the capability of penetrating objects is part of the features of microwaves, there exists, however, a class of 'impenetrable' objects. Rigorously speaking, 'impenetrable' are objects made up of perfect conductors, whereas objects made up of'strong conductors' are 'almost impenetrable', in the sense that the impinging wave penetrates inside the obj ect only to a shallow depth [80]. For such a class of objects, it is thus possible to reconstruct only the objects' shape [81, 82] but not to 'look' inside them. This is what happens at optical frequencies, when the impinging electromagnetic radiation does not significantly penetrate inside objects of which our eyes are capable of seeing only the shape but not the interior. Nevertheless, in the following we refer to penetrable objects only and, therefore, to the reconstruction of their internal features, but we explicitly point out that it is possible to perform an analogous discussion also for impenetrable scatterers.
7.9.2 Formulation of the tomographic approach To understandably illustrate the mathematical equations linking the field measurements to the quantities to be determined (that is, the spatial behaviour of permittivity
a
b
Incident field
Scattering phenomenon
Figure 7.58
Representation of incident and scattered fields
and conductivity) and the difficulties affecting the research of their solution, we will refer to the (mathematically) simpler case when the object is not buried but stands alone in free space. To this end, let us thus consider an electromagnetic field, which we call incident, propagating in free space (Figure 7.58a) when the object to test is initially absent. In such a situation, the incident field is the only solution of Maxwell's equations and propagates while nothing of physical interest happens [80]. If, on the contrary, the object is present, the result of the interaction between the incident field and the object itself is a scattered field (see Figure 7.58b), so that we can express the total field (that is, the field satisfying the Maxwell equations now in presence of the object) as the sum of the incident field plus the scattered one. Basically, the incident wave 'interrogates' the object, which in turn 'answers' through the scattered wave, which depends on the object's nature. For the sake of simplicity, we will consider a 'two-dimensional' geometry, that is we will suppose the object to test to be infinite along the v-direction and with a permittivity dependent only on the x and z co-ordinates (Seq = £Qq(x,z)). We will also assume the incident field radiated by time-harmonic infinitely long and isotropic current filaments parallel to the v-axis and having fixed frequency [81]. In these hypotheses, the equations governing the scattering phenomenon simplify from vectorial to scalar [83]. By considering the situation depicted in Figure 7.58Z?, the equations one arrives at are the following [83]:
(7.106)
As) starting point local minimum
global minimum s
Figure 7.59
A minimisation procedure startingfrom point A and moving according to the decrease of function f(s) converges in a local minimum
(7.107) where H^ (•) is the Hankel function of zero order and the second kind, Es = Es(x,z) is the measured scattered field, 8b and \i are the dielectric permittivity and magnetic permeability of the homogeneous host medium, respectively, kb = co^eb^, £eq = £eq(X z) = s{x, z) — j(cr(x, z)/co) is the equivalent permittivity we are searching for, s and a are the object's dielectric permittivity and conductivity, respectively, co = 2TC/, / being the working frequency, E = E(x, z) is the total field inside the object and Ei = Ei (JC, z) is the incident field. The first equation holds on the measurement points on E and the second inside the object enclosed in the domain £2. The unknown of these equations is the function eeq(x, z), whereas the data are represented by Es. Imaging, or tomographic reconstruction of the object, amounts to solving the above equations for sQq(x, z) when E5 is known [84]. One of the main difficulties in the resolution of (7.106) and (7.107) may be ascribed to the nonlinearity of the relationship between Es and £eqC*> z). This entails that, when the solution is searched for as the equivalent permittivity minimising a cost function accounting for the 'difference' between the measured scattered field and the theoretically predicted one, owing to the nonlinearity of the unknown-data link, such a cost function could exhibit local minima besides the global one. A local minimum could be mistaken, by a minimisation algorithm, for the global one and thus could lead to a 'false solution' [85] (see Figure 7.59). A way to overcome the drawback introduced by nonlinearity is that of employing approximations linearising the relationship between the measurements and the unknown permittivity function (of course, if possible). In particular, if we know a priori that the permittivity of the object under test is sufficiently close to that of
free space, the object is 'small' [86] (where 'small' in electromagnetic applications means with respect to the working wavelength X) and the permittivity has smooth rates of variation [87], then we can deal with it as a 'weak scatterer', in the sense that, from the field's point of view, the presence of the object makes just a little difference with respect to the case in which the object is absent. A visible example of a weak scatterer is a window-pane: indeed, because of its permittivity close to that of air, it introduces just a little perturbation on the propagation of sunbeams which, thus, can enter almost undisturbed inside our houses. For a weak scatterer it is possible to approximate the total field E inside the object as the incident one, thus neglecting the scattered field inside the object itself. Such approximation is known as the 'Born approximation' (Born and Wolf [86], Brancaccio et al. [87] and Slaney et al. [88]). Incidentally, a different linearising approximation of interest in sub-surface applications is the 'distorted Born' approximation [83-89]. It holds when the object, buried beneath the earth's surface, has a permittivity close to that of the host medium. In this case, the field inside the object can be approximated with the field in the host medium in the absence of the object, and thus depends on the medium's permittivity itself. If we suppose to measure the scattered fielder enough from the object, i.e. some wavelengths off the object, then the Born approximation allows us to extract from the scattered field information on the Fourier transform of the unknown equivalent permittivity. Accordingly, the objects that can be 'correctly reconstructed' are those which are not filtered out by the limited performances of the employed tomographic reconstruction procedure, as will be more clear in the sequel. Furthermore, a parameter worth analysing when evaluating the performances of a reconstruction algorithm is resolution [90, 91], i.e. the capability to distinguish nearby objects. Investigating the filtering undergone by the unknown equivalent permittivity and/or the resolution limits is of fundamental importance to appropriately interpret the outcome of reconstructions. What would happen indeed if, having, for instance, no idea of resolution, two landmines were mistaken as one? Knowing resolution would have put us on our guard against the presence of two landmines! In the following Sections, we present some case studies and also describe how the parameters of the measurement configuration help in determining spatial filtering and resolution limits.
7.9.3 Key point of imaging: spatial filtering Let us begin by considering the case in which the object is embedded in free space and suppose that the current filament can assume positions on a circle D surrounding the object as in Figure 1.60a. We measure the scattered field on E for each position assumed by the illuminating current filament on £ itself. We will assume the circle's radius to be great enough such that the transient phenomena are reduced. In this case, it can be shown that the scattered field measurements are related to those Fourier harmonics of the function (sQq(x,z) — £o)/£o contained inside a disk Di of radius 2&o> where ko = 2n/X is the free space wavenumber and £o is the free space dielectric permittivity (see Figure 7.60b). At this point, one could observe that, since
a
b
radiating current filament
C
n receiver For each position of the radiating current filament, the scattered field is measured over all Z Spectral coverage for the measurement configuration in Figure 7.60a. rj and f are the conjugate variables of x and z, respectively
Figure 7.60
Spatial imaging configuration
the scattered field is actually the Fourier transform of (sQq(x,z) — so)/so having a compact support (indeed, (seq(x,z) — so)/so is nonzero only for points inside the object, but vanishes outside of it), such a transform is analytical [78], and thus can be extrapolated outside the disk Di. It seems, thus, to be possible to know the entire Fourier spectrum of the unknown permittivity function. Indeed, one could proceed by calculating successive derivatives of the Fourier transform for some point inside Di and afterwards form a Taylor series. Unfortunately, the analytical extrapolation is an unstable procedure. That is, 'small' errors on the spectrum inside Di, due to the unavoidable presence of noise, could lead to 'large' errors on the prolonged Fourier transform, this last becoming totally unreliable. The result is that the only information about the unknown permittivity function one can extract from these measurements regards approximately just the Fourier harmonics of the permittivity contained inside the above mentioned disk, whereas information referring to the Fourier harmonics contained outside such a disk cannot be restored [92, 93]. In other words, because of the presence of noise on data, approximately no information about the Fourier harmonics outside Di can be extrapolated from the knowledge of the spectrum inside the circle Di itself. Accordingly, if the object's permittivity function has a significant harmonic content inside that circle, the permittivity function will be 'well reconstructed'. If, on the contrary, the unknown permittivity has a significant harmonic content also outside the circle, then only a lowpass version of it will be restored. Moreover, as long as the frequency increases, the extension of the disk containing the retrievable Fourier harmonics of the permittivity function enlarges since its radius 2&o grows with the working frequency. Therefore, the use of higher frequencies would be favourable from this point of view. Unfortunately,
a
radiating current filament
b receiver
X
C
Y] Spectral coverage for the measurement configuration in Figure 7.61a. rj and £ are the conjugate variables of x and z, respectively
Reflection measurement configuration
Figure 7.61
Reflection measurement configuration
when employing higher frequencies one should take account of the fact that this is in conflict with the validity of the Born approximation which, as mentioned above, requires the object to be 'small' with respect to the working wavelength. In the above examined measurement configuration, the object was illuminated all around and the scattered field measurements performed, likewise, all around for each position of the radiating current filament. We now approach a reflection measurement configuration, of major interest in sub-surface applications - that is, suppose we illuminate the object only from one side and measure the scattered field by the same side (see Figure 7.61a). The measurement configuration we are going to refer to is depicted in Figure 7.61a, where transmitters and receivers move across a straight infinitely long line. It is noteworthy that such a measurement configuration is equivalent to that in which the measurement domain is a semicircle. Nevertheless, a straight line has been chosen since it better matches the geometry of a planar air-soil interface, as we will see in the following. We expect further limitations on the recoverable spectrum as compared to those arising in the previous case since a part of the information collected in the former measurement configuration is now no longer exploited. Indeed, in this case the recoverable Fourier spectrum of the permittivity function reduces to the domain D2 as depicted in Figure 7.6Ib, where some 'holes' in the spectral coverage, as compared with Di, now appear. In particular, if we define as 'depth' the direction orthogonal to the measurement line, the permittivity function now approximately undergoes a bandpass spatial filtering in depth and a lowpass spatial filtering along the 'transversal' direction, i.e. along the direction parallel to that of the measurement line. Note how, due to the presence of 'spectral holes' depicted in Figure 7.6IZ? [89], the use of lower frequencies would enable 'filling up' of the holes. When many sets of measurements at different frequencies are used, the extent of the holes depends on the adopted lower frequency. Finally, as in the previous case, the use of a higher frequency improves the extent of the domain D2 still further. So far, we have assumed the object to be embedded in free space. However, situations of interest in sub-surface prospecting require the unknown object to be buried in the ground. To model such a situation, we will suppose the (two-dimensional) space
a
radiating current filament
b receiver
Sub-surface sensing 'reflection measurement configuration'
Spectral coverage for the measurement configuration in Figure 7.62a. r\ and J are the conjugate variables of x and z, respectively
Figure 7.62 Sub-surface reflection measurement configuration
to be divided into two half-spaces separated by a plane interface (Figure 7.62a). The upper half-space, representing the region in which the sensors lie, is free space, whereas the lower half-space, that is the region of space in which the object is embedded, is assumed to consist of a homogeneous and lossless medium having relative dielectric permittivity s^. From a geometrical point of view, the measurement configuration depicted in Figure 7.62a is analogous to that above described, with the difference that now the sensors and the object are separated by the air-soil interface [94]. In contrast with the previous cases, we will now employ the distorted Born approximation to linearise the unknown-data relationship. When the measurement line lies over the air-soil interface (h = 0, see Figure 7.62a), i.e. the sensors are placed over the ground, and the object is buried as deep as at least the wavelength Xt, in the lower half-space (that is, d > Xy, see Figure 7.62a), then the spectral coverage is the same as that in Figure 7.6Ib, provided we replace ko with k^ = co^/s^JIo [89], and the same considerations on the spatial filtering undergone by the permittivity function and on the possibility of extending the covered domain by means of other frequencies still hold. Note that this result is the one we would obtain by also assuming the upper half-space filled by a homogeneous medium having dielectric permittivity equal to £&. On the contrary, when the quota of the measurement line is greater than some free-space wavelengths (h > X)9 then, as may be appreciated by Figure 1.62b, the spectrum undergoes a shrink [87]. In particular, the entity of the shrink is enforced as the permittivity s^ of the lower half-space increases. Indeed, the term 2Jk^ — k$ tends to 2kb as E^ tends to infinity. This is due to the fact that, owing to the total reflection phenomenon, some of the plane waves propagating from the object towards the air-soil interface become evanescent in the upper half-space. These evanescent waves, by decaying exponentially fast while going off from the air-soil interface, reach the measurement line at a negligible level so that the information carried by the corresponding plane wave propagating in the lower half-space is unavoidably lost. Moreover, as the permittivity e^ increases, the total reflection
phenomenon involves an even wider set of directions of propagation, thus justifying the increase of the shrink effect.
7.9.4 Key point of imaging: resolution limits In the previous Section, the influence the measurement configuration has on the performances of the reconstruction algorithm in terms of filtering undergone by the permittivity function has been described and a brief outline on the use of multiple frequencies has been given. Also, we acknowledge that actual measurement configurations require the measurement line to be finite. The performances of the reconstruction procedure can be given in terms of the achievable resolution limits [90], that is in terms of the smallest detail of the unknown permittivity function the reconstruction algorithm is able to distinguish. The aim of this Section is to analyse how the parameters of the measurement configuration, that is the finiteness of the extent of the measurement line and the range of the employed frequencies, affect the performances of the reconstruction algorithm. Our point of view will be focused on the achievable spatial resolution while reconstructing the permittivity function rather than on the spatial filtering it undergoes as done here above. Moreover, we will pursue this goal by referring to simplified situations. In particular, we will assume a finite measurement line and suppose the object to be a dielectric strip embedded in free space and parallel or orthogonal to the measurement line itself (see Figure 7.63a, b). This will allow us to study transversal resolution and depth resolution separately. The measurement line will be assumed to be located in the Fresnel-paraxial zone [86] a
-a
measurement a line
X\
b -a
measurement line
incident plane wave
a
JC
incident plane wave
dielectric strip dielectric strip
z Study of transversal resolution: the case of a dielectric strip parallel to the measurement line
z Study of depth resolution: the case of dielectric strip orthogonal to the measurement line
Figure 7.63
Transversal and depth resolution
with respect to the scattering object, and the Born approximation will once more be assumed. At variance with the cases examined in the previous Section, we assume the impinging field to be a plane wave with fixed angle of incidence. Let us consider first the case depicted in Figure 7.63a in which the dielectric strip is parallel to the measurement line. It can be shown [95] that, if the incident field is at a fixed frequency, the transversal resolution limits Ax while reconstructing the permittivity function s(x) are given by (7.108) In other words, if the dielectric strip were composed of only two point scatterers located at x\ and X2, as depicted in Figure 7.63a, then, following the reconstruction procedure, it would be possible to distinguish them if they were far more than the transversal resolution limits Ax. In the hypothesis of small divergence angle 0, which is reasonable in the Fresnelparaxial zone, the ratio a/zo can be approximated by #, and (7.108) recast as (7.109) As can be seen, resolution improves, that is Ax decreases, as the divergence angle 0 enlarges. This is consistent with the fact that, as 0 enlarges, the extent of the measurement line increases, thus allowing collection of even 'greater amounts of information' about the unknown permittivity function. Note also that the minimum separation by which two scattering points must have to be distinguished does not depend on the position of the scattering points themselves. This can be explained by observing that, in the hypothesis of small divergence angle, the points of the dielectric strip are 'observed' by the sensors on the measurement line under almost the same 'observation angles', as is clarified by Figure 7.63a. Let us now turn to consider the case depicted in Figure 7.63b, where the dielectric strip is orthogonal to the measurement line. It can be shown [96] that, if the incident field is again at a fixed frequency, depth resolution limits Az while reconstructing the permittivity function s(z) are given by (7.110) As may be seen, contrary to the case when the dielectric strip is parallel to the measurement line, depth resolution is now no more uniform along the strip since Az depends on z. In particular, resolution degrades, i.e. Az increases, as z increases. In other words, the spacing by which two point scatterers (see Figure 1.63b) must have to be distinguished by the reconstruction procedure depends on the positions assumed by the point scatterers themselves. In particular, the deeper the location of the point scatterers, the greater the spacing. If we rearrange (7.110) in terms of divergence
angle as follows (see Figure 7.63b), (7.111) then we can explain the worsening in depth of resolution by observing that, as long as a point scatterer is deeper located, it is 'observed' by the sensors under narrower sets of angles (see Figure 7.63b). Accordingly, as long as a point scatterer is more deeply located, the sensors on the measurement line collect even 'lower amounts of information' about it. Roughly speaking, this is what happens to our own eyes: while objects are far away from us we cannot see even larger details. We conclude this 'running shot' on resolution limits by putting a question: what if we employ a set of plane waves having frequencies inside [/min> /max] [97], that is we adopt a 'multi-frequency' illumination? It can be seen [98] that the dependence on depth of resolution can be mitigated by a multi-frequency strategy and depth resolution improved at the same time. In particular, it can be shown that in such a case depth resolution becomes almost independent of z and is given approximately by (7.112) where Amax and Amin are the minimum and maximum wavelengths, respectively, corresponding to the maximum and minimum exploited frequencies / m i n and /max? respectively. Incidentally, note that, through a multi-frequency illumination, depth resolution (7.112) improves as A.min diminishes, whereas, for a fixed Xm\n, it approaches Xm[n/2 as Amax tends to infinity. Equation (7.112) can also be rewritten as (7.113) where Br is the fractional bandwidth [99], defined as (/ max — /min)/2, fc is the mean frequency given by (/max + /min)/2, and kc is the wavelength corresponding to the mean frequency. Finally, when an object having permittivity varying both with x and with z is considered, within the above assumption (Fresnel-paraxial approximation and multifrequency illumination) the above estimates for transverse and depth resolution still hold [100]. We end this Chapter by showing some tomographic reconstruction as reported in Figure 7.64. In particular, Figure 7.64 refers to the measurement configuration having A,max = 1.5A.mm and a = 35A.min. Furthermore, we assume the scattering objects belonging to the rectangular investigation domain Q = [—5Xmin, 5Xmin] x [70A,mm,85A,mm]. Figure 7.64 shows the tomographic reconstructions of two pulse objects located at different depths and with different separation distances. First note that a pulse object is reconstructed as a spot whose size is a measure of the achievable resolution limits. Moreover, the two objects appear well distinct down to a depth separation of 1.5Amin, which is the depth resolution estimate returned by (7.113).
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Figure 7.64
^min
^min
X/Am[n
^min
7.10
c
b
a
^tnin
^min
Reconstruction of two pulse objects at different separation distance: (a) first object located in (O9 74Xmir]u) and second object located in (O9 SOX^n); (b) first object located in (O9 78.5X1nIn^ and second object located in (O9 SOX^n); (c) first object located in (O9 79AjnIn^ and second object located in (O9 80A,miiJ
Minimising clutter
7.10.1 Reduction of unwanted diffractions and reflections from above-surface objects Dr Jan van der Kruk During a GPR survey, special attention must be paid to objects that are present above the earth's surface. Due to the low losses in air and the high wave speed, reflections from above the surface can obscure the sub-surface data and make the interpretation of GPR data a difficult task. The amplitude of these unwanted reflections strongly depends on the radiation characteristics (amplitude and polarisation) of the emitted GPR signals. In Figure 7.65, the amplitude and polarisation of the far-field radiation patterns generated by a dipole antenna [101] are compared with the results for the total field, which are obtained by evaluating the integral expressions. Although the far-field radiation pattern is a reasonable approximation to that of the total field, there is a significant error near the critical angle 0c and near the interface. The vertically polarised total-field has a relatively large amplitude near the interface in the upper half-space in the E-plane, whereas the horizontally polarised total-field has a small amplitude near the interface in the H-plane (Figure 7.65). A consequence of these radiation characteristics is that strong reflections arise from vertical-standing objects in the E -plane of the antennas. Atypical example of abovesurface reflections is shown in Figure 7.66. The measurements were carried out with the trees present in the E-plane of both antennas. The large hyperbolas with gently dipping tails are diffractions from the trees, whereas the small hyperbolas with steeply dipping tails are diffractions from pipes present in the sub-surface. The CMP results depicted in Figure 7.66c show that events 3 and 4 have small moveouts, indicating that they have travelled with the speed of light. It is expected that the amplitudes of diffractions from the same trees would be markedly smaller when they are present in the //-plane of the antennas, because the polarisation of the electric field is then perpendicular to them and amplitudes near the interface in the //-plane are smaller than those in the £-plane. The results
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Figure 7.64
^min
^min
X/Am[n
^min
7.10
c
b
a
^tnin
^min
Reconstruction of two pulse objects at different separation distance: (a) first object located in (O9 74Xmir]u) and second object located in (O9 SOX^n); (b) first object located in (O9 78.5X1nIn^ and second object located in (O9 SOX^n); (c) first object located in (O9 79AjnIn^ and second object located in (O9 80A,miiJ
Minimising clutter
7.10.1 Reduction of unwanted diffractions and reflections from above-surface objects Dr Jan van der Kruk During a GPR survey, special attention must be paid to objects that are present above the earth's surface. Due to the low losses in air and the high wave speed, reflections from above the surface can obscure the sub-surface data and make the interpretation of GPR data a difficult task. The amplitude of these unwanted reflections strongly depends on the radiation characteristics (amplitude and polarisation) of the emitted GPR signals. In Figure 7.65, the amplitude and polarisation of the far-field radiation patterns generated by a dipole antenna [101] are compared with the results for the total field, which are obtained by evaluating the integral expressions. Although the far-field radiation pattern is a reasonable approximation to that of the total field, there is a significant error near the critical angle 0c and near the interface. The vertically polarised total-field has a relatively large amplitude near the interface in the upper half-space in the E-plane, whereas the horizontally polarised total-field has a small amplitude near the interface in the H-plane (Figure 7.65). A consequence of these radiation characteristics is that strong reflections arise from vertical-standing objects in the E -plane of the antennas. Atypical example of abovesurface reflections is shown in Figure 7.66. The measurements were carried out with the trees present in the E-plane of both antennas. The large hyperbolas with gently dipping tails are diffractions from the trees, whereas the small hyperbolas with steeply dipping tails are diffractions from pipes present in the sub-surface. The CMP results depicted in Figure 7.66c show that events 3 and 4 have small moveouts, indicating that they have travelled with the speed of light. It is expected that the amplitudes of diffractions from the same trees would be markedly smaller when they are present in the //-plane of the antennas, because the polarisation of the electric field is then perpendicular to them and amplitudes near the interface in the //-plane are smaller than those in the £-plane. The results
Figure 7.65 Comparison of total-field and far-field amplitudes of the spherical electric field components EQ in the E-plane (left) and E